Solution: Assume $f(x)=\sec x$ So, $f(x)=\frac{1}{\cos x}$ $f(x)$ is not defined when $\cos x=0$ And $\cos x=0$ when, $x=\frac{\pi}{2}$ and odd multiples of $\frac{\pi}{2}$ like $-\frac{\pi}{2}$...
Show that function $f(x)=\left\{\begin{array}{r}\frac{x^{n}-1}{x-1}, \text { when } x \neq 1 \text {; } \\ n, \text { when } x=1\end{array}\right.$
Solution: It is given that: $f(x)=\left\{\begin{array}{c} \frac{x^{n}-1}{x-1}, \text { when } x \neq 1 \\ n, \text { when } x=1 \end{array}\right.$ L.H.L. and $\mathrm{x}=1$ $\begin{array}{l} \lim...
Find the value of x, given that A^2 = B,
Solution: So, on comparison we get \[x\text{ }=\text{ }36.\]
If given matrix, find the matrix X such that: A + X = 2B + C
Solution: As per the given question,
If given matrix, find the matrix ‘X’ and matrix ‘Y’.
Solution: Now, On comparison, we get \[-28\text{ }-\text{ }3x\text{ }=\text{ }10\] \[3x\text{ }=\text{ }-38\] \[x\text{ }=\text{ }-38/3\] And, \[20\text{ }-\text{ }3y\text{ }=\text{ }-8\] \[3y\text{...
Find x and y, if:
Solution: According to the given question, On comparison, we get \[2x\text{ }+\text{ }3x\text{ }=\text{ }5\] And \[2y\text{ }+\text{ }4y\text{ }=\text{ }12\] \[5x\text{ }=\text{ }5\text{ }and\text{...
Solve: (i) A (BA) (ii) (AB) B.
Solution: \[\left( i \right)\text{ }A\text{ }\left( BA \right)\] \[\left( ii \right)\text{ }\left( AB \right)\text{ }B\]
Find the values of a, b and c.
Solution: According to the given ques, On comparison, we get \[a\text{ }+\text{ }1\text{ }=\text{ }5\Rightarrow a\text{ }=\text{ }4\] \[b\text{ }+\text{ }2\text{ }=\text{ }0\Rightarrow b\text{...
3A x M = 2B; find matrix M.
Solution: According to the given question, \[3A\text{ }x\text{ }M\text{ }=\text{ }2B\] Suppose the order of the \[matrix\text{ }M\text{ }be\text{ }\left( a\text{ }x\text{ }b \right)\] Now, we know...
Evaluate:
Solution: As per the given question,
Solve: (i) The order of the matrix X. (ii) The matrix X.
Solution: (i) Suppose, the order of the matrix be \[a\text{ }x\text{ }b\] We know that Hence, for product of matrices to be possible \[a\text{ }=\text{ }2\] And, form the order of the resultant...
If given matrix , find x and y, if: (i) x, y ∈ W (whole numbers) (ii) x, y ∈ Z (integers)
Solution: According to the given question, \[{{x}^{2}}~+\text{ }{{y}^{2}}~=\text{ }25\] And, \[-2{{x}^{2}}~+\text{ }{{y}^{2}}~=\text{ }-2\] \[\left( i \right)\text{ }x,\text{ }y~\in ~W\text{ }\left(...
Find x and y, if:
Solution: On comparison, we get \[3x\text{ }+\text{ }18\text{ }=\text{ }15\] And \[12x\text{ }+\text{ }77\text{ }=\text{ }10y\] \[3x\text{ }=\text{ }-3\] And \[y\text{ }=\text{ }\left( 12x\text{...
Find x and y, if:
Solution: On comparison, we get \[6x\text{ }-\text{ }10\text{ }=\text{ }8\] And \[-2x\text{ }+\text{ }14\text{ }=\text{ }4y\] \[6x\text{ }=\text{ }18\] And \[y\text{ }=\text{ }\left( 14\text{...
If the given matrix. simplify: A2 + BC.
Solution: \[{{A}^{2}}~+\text{ }BC\]
If given matrix. Then show that: (i) A(B + C) = AB + AC (ii) (B – A)C = BC – AC.
Solution: \[\left( i \right)\text{ }A\left( B\text{ }+\text{ }C \right)\] \[AB\text{ }+\text{ }AC\] So, \[A\left( B\text{ }+\text{ }C \right)\text{ }=\text{ }AB\text{ }+\text{ }AC\] \[\left( ii...
If given matrix and A2 = I, find a and b.
Solution: \[{{A}^{2}}\] Given, \[~{{A}^{2~}}=\text{ }I\] On comparison, we get \[1\text{ }+\text{ }a\text{ }=\text{ }1\] \[a\text{ }=\text{ }0\] And, \[-1\text{ }+\text{ }b\text{ }=\text{ }0\]...
Find the matrix A, if B =given matrix and B2 = B + ½A.
Solution: \[{{B}^{2}}\] \[{{B}^{2}}~=\text{ }B\text{ }+\text{ }{\scriptscriptstyle 1\!/\!{ }_2}A\] \[{\scriptscriptstyle 1\!/\!{ }_2}A\text{ }=\text{ }{{B}^{2}}-\text{ }B\] \[A\text{ }=\text{...
Solve : (i) (A + B)^2 (ii) A2 + B2
Solution: According to the given ques, \[\left( i \right)\text{ }\left( A\text{ }+\text{ }B \right)\] \[So,\text{ }{{\left( A\text{ }+\text{ }B \right)}^{2}}~=\text{ }\left( A\text{ }+\text{ }B...
Solve: (i) AB (ii) A^2 – AB + 2B
Solution: \[\left( \mathbf{i} \right)\text{ }\mathbf{AB}\text{ }\] \[\left( ii \right)\text{ }{{\mathbf{A}}^{\mathbf{2}}}-\text{ }\mathbf{AB}\text{ }+\text{ }\mathbf{2B}\]
Solve: (i) A – B (ii) A^2
Solution: \[\left( \mathbf{i} \right)\text{ }\mathbf{A}\text{ }-\text{ }\mathbf{B}\text{ }\] \[\text{ }\left( \mathbf{ii} \right)\text{ }{{\mathbf{A}}^{\mathbf{2}~}}\]
BA = M^2, find the values of a and b.
Solution: $BA$ \[{{M}^{2}}\] So, \[BA\text{ }={{M}^{2}}\] On comparison, we get \[-2b\text{ }=\text{ }-2\] \[b\text{ }=\text{ }1\] And, \[a\text{ }=\text{ }2\]
If the given matrix and I is a unit matrix of the same order as that of M; show that: M2 = 2M + 3I
Solution: \[{{M}^{2}}\] \[2M\text{ }+\text{ }3I\] Hence, \[{{M}^{2}}~=\text{ }2M\text{ }+\text{ }3I\]
Find A2 + AC – 5B
Solution: \[{{A}^{2}}\] $AC$ $5B$ \[{{A}^{2}}~+\text{ }AC\text{ }-\text{ }5B\text{ }=\]
Is the following possible: A^2
Solution: \[{{A}^{2}}~=\text{ }A\text{ }x\text{ }A,\text{ }\]isn’t possible because the number of columns isn’t equal to its number of rows in matrix A.
Is the following possible: (i) AB (ii) BA
Solution: \[\left( i \right)\text{ }AB\] \[\left( ii \right)\text{ }BA\]
Solve: (i) (AB) C (ii) A (BC)
Solution: According to the given ques, \[\left( i \right)\text{ }\left( AB \right)\] \[\left( AB \right)\text{ }C\] \[\left( ii \right)\text{ }BC\] \[A\text{ }\left( BC \right)\] So, \[\text{...
Find x and y, if:
Solution: (i) On comparison, we get \[5x\text{ }-\text{ }2\text{ }=\text{ }8\] \[5x\text{ }=\text{ }10\] \[x\text{ }=\text{ }2\] And, \[20\text{ }+\text{ }3x\text{ }=\text{ }y\] \[20\text{ }+\text{...
If find x and y when x and y when A2 = B.
Solution: \[{{A}^{2}}~\] \[{{A}^{2}}~=\text{ }B\] On comparison, we get \[4x\text{ }=\text{ }16\] \[x\text{ }=\text{ }4\] And, \[1\text{ }=\text{ }-y\] \[y\text{ }=\text{ }-1\]
If the given matrix and I is a unit matrix of order 2×2, find: (i) A^2 (ii) B^2A
Solution: (i) \[{{A}^{2}}\] (ii) \[~{{B}^{2}}\] \[{{B}^{2}}A\]
If the given matrix and I is a unit matrix of order 2×2, find: (i) AI (ii) IB
Solution: (i) AI = (ii) IB=
If given matrix and I is a unit matrix of order 2×2, find: (i) AB (ii) BA
Solution: According to the given question (i) (ii)
Evaluate: if possible: If not possible, give reason.
Solution: The product of the given matrices isn’t possible as per the rule the number of columns in the first matrix isn’t equal to the number of rows in the second matrix.
Evaluate: if possible: If not possible, give reason.
Solution: \[=\text{ }\left[ 6\text{ }+\text{ }0 \right]\text{ }=\text{ }\left[ 6 \right]\] \[=\text{ }\left[ -2+2\text{ }3-8 \right]\text{ }=\text{ }\left[ 0\text{ }-5 \right]\]
(i) find the matrix 2A + B. (ii) find a matrix C such that:
(ii) Solution: (i) \[2A\text{ }+\text{ }B\] (ii)
Solve:
Solution: According to the given question, the matrix is
From given data below find (i) 2A – 3B + C (ii) A + 2C – B
Solution: \[\left( i \right)\text{ }2A\text{ }-\text{ }3B\text{ }+\text{ }C\] \[\left( ii \right)\text{ }A\text{ }+\text{ }2C\text{ }-\text{ }B\]
Find x and y if: (i) 3[4 x] + 2[y -3] = [10 0]
(ii) Solution: From L.H.S, we have \[3\left[ 4\text{ }x \right]\text{ }+\text{ }2\left[ y\text{ }-3 \right]\] \[=\text{ }\left[ 12\text{ }3x \right]\text{ }+\text{ }\left[ 2y\text{ }-6 \right]~\]...
Evaluate:
(I) (ii) Solution: According to the given ques, (i) (ii)
Evaluate: (i) 3[5 -2]
(ii) Solution: (i) \[3\left[ 5\text{ }-2 \right]\text{ }=\text{ }\left[ 3\times 5\text{ }3x-2 \right]\text{ }=\text{ }\left[ 15\text{ }-6 \right]\] (ii)
Find : (i) A + B – C (ii) A – B +C
If A= , B= , C= Answer (i) (ii)
Find: (i) B + C (ii) A – C
If A= , B = , C= Answer (i) \[B\text{ }+\text{ }C\text{ }=~\] (ii) \[A\text{ }-\text{ }C\text{ }=\]
If A = [8 -3] and B = [4 -5]; find: (i) A + B (ii) B – A
(i) \[A\text{ }+\text{ }B\text{ }=\text{ }\left[ 8\text{ }-3 \right]\text{ }+\text{ }\left[ 4\text{ }-5 \right]\] \[~=\text{ }\left[ 8+4\text{ }-3-5 \right]\text{ }=\text{ }\left[ 12\text{ }-8...
Solve for a, b and c if
(i) (ii) Answer:- In the event that two networks are supposed to be equivalent, their comparing components are additionally equivalent. In this manner, (i) \[a\text{ }+\text{ }5\text{ }=\text{...
In the given figure find x, y and z.
Answer Two matrices are said to be equal, when their corresponding elements are also equal. So, \[x\text{ }=\text{ }3,\] \[y\text{ }+\text{ }2\text{ }=\text{ }1~so,\text{ }y\text{ }=\text{ }-1\]...
State, whether the following statements are true or false. If false, give a reason. A column matrix has many columns and one row.
False A section framework has just a single segment and many lines.
State, whether the following statements are true or false. If false, give a reason. (i) Transpose of a 2 x 1 matrix is a 2 x 1 matrix. (ii) Transpose of a square matrix is a square matrix.
(I) False. The amount of grids\[A+B\] is conceivable just when the request for both the frameworks \[A\text{ }and\text{ }B\]are same. (ii) True
State, whether the following statements are true or false. If false, give a reason. (i) If A and B are two matrices of orders 3 x 2 and 2 x 3 respectively; then their sum A + B is possible. (ii) The matrices A2 x 3 and B2 x 3 are conformable for subtraction.
(I) False. The amount of grids \[A\text{ }+\text{ }B\] is conceivable just when the request for both the frameworks \[A\text{ }and\text{ }B\]are same. (ii) True