Exercise 5C Archives

If $\left[\begin{array}{cc}2 & 3 \\ 5 & 7\end{array}\right]\left[\begin{array}{cc}1 & -3 \\ -2 & 4\end{array}\right]=\left[\begin{array}{cc}-4 & 6 \\ -9 & \mathrm{x}\end{array}\right]$, find the value of $\mathrm{x}$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{ll}2 & 3 \\ 5 & 7\end{array}\right), B=\left(\begin{array}{cc}1 & -3 \\ -2 & 4\end{array}\right)$ and $C=\left(\begin{array}{cc}-4 & 6 \\...

If $A=\left[\begin{array}{cc}1 & 0 \\ -1 & 7\end{array}\right]$ and $B=\left[\begin{array}{cc}0 & 4 \\ -1 & 7\end{array}\right]$, find $\left(3 A^{2}-2 B+1\right)$.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{cc}1 & 0 \\ -1 & 7\end{array}\right), B=\left(\begin{array}{cc}0 & 4 \\ -1 & 7\end{array}\right)$. (i) Let's compute first $A^{2}$ $A^{2}=A...

Give an example of three matrices A, B, C such that AB = AC but B ≠ C.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A B}=\boldsymbol{A} \boldsymbol{C}$ but $\boldsymbol{B} \neq \boldsymbol{C}$. WE need to find: $\boldsymbol{A}, \boldsymbol{B}$. Let's take...

Given an example of two matrices A and B such that A ≠ O, B ≠ O, AB = O and BA ≠ O.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A} \neq \boldsymbol{O}, \boldsymbol{B} \neq \boldsymbol{O}, \boldsymbol{A B}=\boldsymbol{O}$ and $\boldsymbol{B A} \neq \boldsymbol{O}$. We need to find:...

If $\mathrm{A}=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$, prove that $\mathrm{A}^{\mathrm{n}}=\left[\begin{array}{ll}1 & \mathrm{n} \\ 0 & 1\end{array}\right]$ for all $\mathrm{n} \in \mathrm{N}$.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{ll}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1}\end{array}\right)$. We need to show: $A^{n}=\left(\begin{array}{ll}1 & n \\ 0...

If $A=\left[\begin{array}{cc}3 & 4 \\ -4 & -3\end{array}\right]$, find $f(A)$, where $f(x)=x 2-5 x+7$.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{cc}3 & 4 \\ -4 & -3\end{array}\right)$ and equation $f(x)=x^{2}-5 x+7$. (i) Let us compute first $A^{2}$ $A^{2}=A A=\left(\begin{array}{cc} 3 & 4...

Find the values of $a$ and $b$ for which $\left[\begin{array}{cc} a & b \\ -a & 2 b \end{array}\right]\left[\begin{array}{c} 2 \\ -1 \end{array}\right]=\left[\begin{array}{l} 5 \\ 4 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{cc}\boldsymbol{a} & \boldsymbol{b} \\ -\boldsymbol{a} & \boldsymbol{2} \boldsymbol{b}\end{array}\right),...

If $\left[\begin{array}{lll}x & 4 & 1\end{array}\right]\left[\begin{array}{ccc}2 & 1 & 2 \\ 1 & 0 & 2 \\ 0 & 2 & -4\end{array}\right]\left[\begin{array}{c}x \\ 4 \\ -1\end{array}\right]=\mathrm{O}$, find $x$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{ccc}2 & 1 & 2 \\ 1 & 0 & 2 \\ 0 & 2 & -4\end{array}\right), B=\left(\begin{array}{lll}x & 4 & 1\end{array}\right)$ and...

If $\left[\begin{array}{lll}1 & x & 1\end{array}\right]\left[\begin{array}{ccc}1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & 2 & 5\end{array}\right]\left[\begin{array}{c}1 \\ -2 \\ 3\end{array}\right]=\mathrm{O}$, find $x$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & 2 & 5\end{array}\right), B=\left(\begin{array}{lll}1 & x & 1\end{array}\right)$ and...

If $A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right]$, show that $A^{2}=\left[\begin{array}{cc}\cos 2 \alpha & \sin 2 \alpha \\ -\sin 2 \alpha & \cos 2 \alpha\end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right)$ and to show $A^{2}=$ $\left(\begin{array}{cc}\cos ^2 \alpha & \sin...

If $F(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]$, show that $F(x) \cdot F(y)=F(x+y)$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{F}(\boldsymbol{X})=\left(\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right)$ and to show...

If $A=\left[\begin{array}{rr}1 & -1 \\ 2 & -1\end{array}\right], B=\left[\begin{array}{rr}a & -1 \\ b & -1\end{array}\right]$ and $(A+B)^{2}=\left(A^{2}+B^{2}\right)$ then find the values of $a$ and $b$.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{ll}1 & -1 \\ 2 & -1\end{array}\right), B=\left(\begin{array}{ll}a & -1 \\ b & -1\end{array}\right)$ and $(A+B)^{2}=\left(A^{2}+\right.$...

Find the matrix A such that A. $\left[\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right]=\left[\begin{array}{cc}0 & -4 \\ 10 & 3\end{array}\right]$.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{B}=\left(\begin{array}{ll}\mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5}\end{array}\right)$ and $\boldsymbol{C}=\left(\begin{array}{cc}\mathbf{0} &...

Find the matrix A such that $\left[\begin{array}{cc}5 & -7 \\ -2 & 3\end{array}\right] \cdot \mathrm{A}=\left[\begin{array}{cc}-16 & -6 \\ 7 & 2\end{array}\right]$.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{B}=\left(\begin{array}{cc}\mathbf{5} & -\mathbf{7} \\ -\mathbf{2} & \mathbf{3}\end{array}\right)$ and $\boldsymbol{C}=\left(\begin{array}{cc}-\mathbf{1 6}...

If $A=\left[\begin{array}{ll}3 & 2 \\ 1 & 1\end{array}\right]$, find the value of a and $b$ such that $A^{2}+a A+b l=0$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{ll}\mathbf{3} & \mathbf{2} \\ \mathbf{1} & \mathbf{1}\end{array}\right)$. To find $\boldsymbol{a}, \boldsymbol{b}$ such that...

If $A=\left[\begin{array}{ll}3 & 1 \\ 7 & 5\end{array}\right]$, find $x$ and $y$ such that $A^{2}+x \mid=y A$.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{ll}\mathbf{3} & \mathbf{1} \\ \mathbf{7} & \mathbf{5}\end{array}\right)$. To find $\boldsymbol{x}, \boldsymbol{y}$ such that...

Solve for $x$ and $y$, when $\left[\begin{array}{cc} 3 & -4 \\ 1 & 2 \end{array}\right]\left[\begin{array}{l} \mathrm{x} \\ \mathrm{y} \end{array}\right]=\left[\begin{array}{l} 3 \\ 11 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{cc}3 & -4 \\ 1 & 2\end{array}\right), B=\left(\begin{array}{c}3 \\ 11\end{array}\right)$ and $X=\left(\begin{array}{l}x \\ y\end{array}\right)$. We...

Find the values of $x$ and $y$, when $\left[\begin{array}{cc} 2 & -3 \\ 1 & 1 \end{array}\right]\left[\begin{array}{l} \mathrm{x} \\ \mathrm{y} \end{array}\right]=\left[\begin{array}{l} 1 \\ 3 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{cc}2 & -3 \\ 1 & 1\end{array}\right), B=\left(\begin{array}{l}1 \\ 3\end{array}\right)$ and $X=\left(\begin{array}{l}x \\ y\end{array}\right)$. To...

If $A=\left[\begin{array}{cc}1 & 2 \\ 4 & -3\end{array}\right]$ and $f(x)=2 x^{3}+4 x+5$, find $f(A)$.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{cc}\mathbf{1} & \mathbf{2} \\ \mathbf{4} & \mathbf{- 3}\end{array}\right)$. Now addition/subtraction of two matrices is possible if...

If $A=\left[\begin{array}{cc}-1 & 2 \\ 3 & 1\end{array}\right]$, find $f(A)$, where $f(x)=x^{2}-2 x+3$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{cc}-1 & 2 \\ 3 & 1\end{array}\right)$. Now addition/subtraction of two matrices is possible if order of both the matrices are same and...

If $A=\left[\begin{array}{rr}3 & -2 \\ 4 & -2\end{array}\right]$, find $k$ so that $A^{2}=k A-21$.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{ll}\mathbf{3} & -\mathbf{2} \\ \mathbf{4} & -\mathbf{2}\end{array}\right)$. Now addition/subtraction of two matrices is possible if...

Show that the matrix $\mathrm{A}=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]$ satisfies the equation $\mathrm{A}^{3}-4 \mathrm{~A}^{2}+\mathrm{A}=0$.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{ll}\mathbf{2} & \mathbf{3} \\ \mathbf{1} & \mathbf{2}\end{array}\right)$. Now addition of two matrices is possible if order of both the...

If $A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]$, show that $(A 2-5 A+71)=0$.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{cc}\mathbf{3} & \mathbf{1} \\ -\mathbf{1} & \mathbf{2}\end{array}\right)$. Now addition of two matrices is possible if order of both the...

If $A=\left[\begin{array}{cc}2 & -2 \\ -3 & 4\end{array}\right]$ then find $\left(-A^{2}+6 A\right)$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{cc}\mathbf{2} & \mathbf{- 2} \\ -\mathbf{3} & \mathbf{4}\end{array}\right)$. Now addition of two matrices is possible if order of both...

If $A=\left[\begin{array}{cc}2 & -1 \\ 3 & 2\end{array}\right]$ and $B=\left[\begin{array}{cc}0 & 4 \\ -1 & 7\end{array}\right]$, find $\left(3 A^{2}-2 B+1\right)$.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{cc}\mathbf{2} & \mathbf{- 1} \\ \mathbf{3} & \mathbf{2}\end{array}\right)$ and $\boldsymbol{B}=\left(\begin{array}{cc}\mathbf{0} &...

If $A=\left[\begin{array}{ccc}4 & -1 & -4 \\ 3 & 0 & -4 \\ 3 & -1 & -3\end{array}\right]$, show that $A^{2}=1$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{ccc}\mathbf{4} & -\mathbf{1} & -\mathbf{4} \\ \mathbf{3} & \mathbf{0} & -\mathbf{4} \\ \mathbf{3} & -\mathbf{1} &...

If $A=\left[\begin{array}{ccc}2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3\end{array}\right]$, show that $A^{2}=A$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{ccc}\mathbf{2} & \mathbf{- 2} & -\mathbf{4} \\ \mathbf{- 1} & \mathbf{3} & \mathbf{4} \\ \mathbf{1} & -\mathbf{2} &...

If $A=\left[\begin{array}{cc}a b & b^{2} \\ -a^{2} & -a b\end{array}\right]$, show that $A^{2}=0$.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{cc}\boldsymbol{a} \boldsymbol{b} & \boldsymbol{b}^{2} \\ -\boldsymbol{a}^{2} & -\boldsymbol{a} \boldsymbol{b}\end{array}\right) .$ To...

If $A=\left[\begin{array}{ccc}1 & 0 & -2 \\ 3 & -1 & 0 \\ -2 & 1 & 1\end{array}\right], B=\left[\begin{array}{ccc}0 & 5 & -4 \\ -2 & 1 & 3 \\ 1 & 0 & 2\end{array}\right]$ and $C=\left[\begin{array}{ccc}1 & 5 & 2 \\ -1 & 1 & 0 \\ 0 & -1 & 1\end{array}\right] ;$ verify that $A(B-C)=(A B-A C)$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{ccc}1 & 0 & 2 \\ 3 & -1 & 0 \\ -2 & 1 & 1\end{array}\right), B=\left(\begin{array}{ccc}0 & 5 & -4 \\ -2 & 1 & 3 \\ 1...

Verify that $A(B+C)=(A B+A C)$, when $\mathrm{A}=\left[\begin{array}{cc} 2 & 3 \\ -1 & 4 \\ 0 & 1 \end{array}\right], \mathrm{B}=\left[\begin{array}{cc} 5 & -3 \\ 2 & 1 \end{array}\right] \text { and } \mathrm{C}=\left[\begin{array}{cc} -1 & 2 \\ 3 & 4 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{cc}2 & 3 \\ -1 & 4 \\ 0 & 1\end{array}\right), B=\left(\begin{array}{cc}5 & -3 \\ 2 & 1\end{array}\right)$. and...

Verify that $A(B+C)=(A B+A C)$, when $\mathrm{A}=\left[\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right], \mathrm{B}=\left[\begin{array}{cc} 2 & 0 \\ 1 & -3 \end{array}\right] \text { and } \mathrm{C}=\left[\begin{array}{cc} 1 & -1 \\ 0 & 1 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right), \boldsymbol{B}=\left(\begin{array}{cc}\mathbf{2} &...

For the following matrices, verify that $A(B C)=(A B) C$ : $\mathrm{A}=\left[\begin{array}{ccc} 2 & 3 & -1 \\ 3 & 0 & 2 \end{array}\right], \mathrm{B}=\left[\begin{array}{l} 1 \\ 1 \\ 2 \end{array}\right] \text { and } \mathrm{C}=\left[\begin{array}{ll} 1 & -2 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{ccc}\mathbf{2} & \mathbf{3} & \mathbf{- 1} \\ \mathbf{3} & \mathbf{0} & \mathbf{2}\end{array}\right),...

For the following matrices, verify that $A(B C)=(A B) C$ : $\mathrm{A}=\left[\begin{array}{lll} 1 & 2 & 5 \\ 0 & 1 & 3 \end{array}\right], \mathrm{B}=\left[\begin{array}{lll} 2 & 3 & 0 \\ 1 & 0 & 4 \\ 1 & -1 & 2 \end{array}\right] \text { and } \mathrm{C}=\left[\begin{array}{l} 1 \\ 4 \\ 5 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{lll}1 & 2 & 5 \\ 0 & 1 & 3\end{array}\right), B=\left(\begin{array}{ccc}2 & 3 & 0 \\ 1 & 0 & 4 \\ 1 & -1 &...

If $A=\left[\begin{array}{ccc}0 & c & -b \\ -c & 0 & a \\ b & -a & 0\end{array}\right]$ and $B=\left[\begin{array}{lll}a^{2} & a b & a c \\ a b & b^{2} & b c \\ a c & b c & c^{2}\end{array}\right]$. show that $A B$ is a zero matrix.

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{ccc}\mathbf{0} & \boldsymbol{c} & -\boldsymbol{b} \\ -\boldsymbol{c} & \mathbf{0} & \boldsymbol{a} \\ \boldsymbol{b} &...

$\text { If } A=\left[\begin{array}{ccc} 2 & -3 & -5 \\ -1 & 4 & 5 \\ 1 & -3 & -4 \end{array}\right] \text { and } B=\left[\begin{array}{ccc} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{array}\right] \text {, shown that } A B=A \text { and } B A=B \text {. }$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{ccc}\mathbf{2} & -\mathbf{3} & -\mathbf{5} \\ -\mathbf{1} & \mathbf{4} & \mathbf{5} \\ \mathbf{1} & -\mathbf{3} &...

Show that $A B=B A$ in each of the following cases: $A=\left[\begin{array}{ccc} 1 & 3 & -1 \\ 2 & 2 & -1 \\ 3 & 0 & -1 \end{array}\right] \text { and } B=\left[\begin{array}{ccc} -2 & 3 & -1 \\ -1 & 2 & -1 \\ -6 & 9 & -4 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{ccc}\mathbf{1} & \mathbf{3} & -\mathbf{1} \\ \mathbf{2} & \mathbf{2} & -\mathbf{1} \\ \mathbf{3} & \mathbf{0} &...

Show that $A B=B A$ in each of the following cases: $\mathrm{A}=\left[\begin{array}{lll} 1 & 2 & 1 \\ 3 & 4 & 2 \\ 1 & 3 & 2 \end{array}\right] \text { and } \mathrm{B}=\left[\begin{array}{ccc} 10 & -4 & -1 \\ -11 & 5 & 0 \\ 9 & -5 & 1 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{lll}1 & 2 & 1 \\ 3 & 4 & 2 \\ 1 & 3 & 2\end{array}\right)$ and $B=\left(\begin{array}{ccc}10 & -4 & -1 \\ -11 & 5 & 0...

Show that $A B=B A$ in each of the following cases: $A=\left[\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right] \text { and } B=\left[\begin{array}{cc} \cos \phi & -\sin \phi \\ \sin \phi & \cos \phi \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $A=\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right)$ and $B=\left(\begin{array}{cc}\cos \phi & -\sin \phi \\ \sin \phi...

Show that $A B \neq B A$ in each of the following cases: $\mathrm{A}=\left[\begin{array}{lll} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{array}\right] \text { and } \mathrm{B}=\left[\begin{array}{ccc} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{lll}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{0} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{1} &...

Show that $A B \neq B A$ in each of the following cases : $A=\left[\begin{array}{cc} 5 & -1 \\ 6 & 7 \end{array}\right] \text { and } B=\left[\begin{array}{ll} 2 & 1 \\ 3 & 4 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{cc}\mathbf{5} & -\mathbf{1} \\ \mathbf{6} & \mathbf{7}\end{array}\right)$ and $\boldsymbol{B}=\left(\begin{array}{ll}\mathbf{2} &...

Compute $A B$ and $B A$, which ever exists when $A=\left[\begin{array}{cc} 2 & 1 \\ 3 & 2 \\ -1 & 1 \end{array}\right] \text { and } B=\left[\begin{array}{rrr} 1 & 0 & 1 \\ -1 & 2 & 1 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{B}=\left(\begin{array}{ccc}\mathbf{1} & \mathbf{0} & \mathbf{1} \\ -\mathbf{1} & \mathbf{2} & \mathbf{1}\end{array}\right)$ and...

Compute $A B$ and BA, which ever exists when $A=\left[\begin{array}{lll} 1 & 2 & 3 & 4 \end{array}\right] \text { and } B=\left[\begin{array}{l} 1 \\ 2 \\ 3 \\ 4 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{llll}\mathbf{1} & 2 & 3 & 4\end{array}\right)$ and $\boldsymbol{B}=\left(\begin{array}{l}\mathbf{1} \\ \mathbf{2} \\ \mathbf{3} \\...

Compute AB and BA, which ever exists when $\mathrm{A}=\left[\begin{array}{rrr} 0 & 1 & -5 \\ 2 & 4 & 0 \end{array}\right] \text { and } \mathrm{B}=\left[\begin{array}{cc} 1 & 3 \\ -1 & 0 \\ 0 & 5 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{ccc}\mathbf{0} & \mathbf{1} & -\mathbf{5} \\ \mathbf{2} & \mathbf{4} & \mathbf{0}\end{array}\right)$ and...

Compute AB and BA, which ever exists when $\mathrm{A}=\left[\begin{array}{cc} -1 & 1 \\ -2 & 2 \\ -3 & 3 \end{array}\right] \text { and } \mathrm{B}=\left[\begin{array}{ccc} 3 & -2 & 1 \\ 0 & 1 & 2 \\ -3 & 4 & -5 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{cc}-\mathbf{1} & \mathbf{1} \\ -\mathbf{2} & \mathbf{2} \\ -\mathbf{3} & \mathbf{3}\end{array}\right)$ and...

Compute AB and BA, which ever exists when $A=\left[\begin{array}{cc} 2 & -1 \\ 3 & 0 \\ -1 & 4 \end{array}\right] \text { and } B=\left[\begin{array}{cc} -2 & 3 \\ 0 & 4 \end{array}\right]$

CBSE, Class 12, Exercise 5C, Maths, Matrices, RS Aggarwal

Solution: We have $\boldsymbol{A}=\left(\begin{array}{cc}\mathbf{2} & \mathbf{- 1} \\ \mathbf{3} & \mathbf{0} \\ \mathbf{- 1} & \mathbf{4}\end{array}\right)$ and...