Answer: Given, \[matrix\text{ }A\text{ }=\text{ }matrix\text{ }B\] Then, at that point, their comparing components are equivalent. Thus, we have \[{{a}_{11}}~=\text{ }{{b}_{11}};\]\[a\text{ }+\text{...
If $\left[ \begin{matrix} 2a+b & c \\ d & 3a-b \\ \end{matrix} \right]=\left[ \begin{matrix} 4 & 3a \\ 7 & 6 \\ \end{matrix} \right]$, find the values of a, b, c and d
It is given that $\left[ \begin{matrix} 2a+b & c \\ d & 3a-b \\ \end{matrix} \right]=\left[ \begin{matrix} 4 & 3a \\ 7 & 6 \\ \end{matrix} \right]$ Then, $2a+b=4$ … [equation...
If $X=\left[ \begin{matrix} p & q \\ 8 & 5 \\ \end{matrix} \right],Y=\left[ \begin{matrix} 3p & 5q \\ 2q & 7 \\ \end{matrix} \right]$and $X+Y=\left[ \begin{matrix} 12 & 6 \\ 2r & 3s \\ \end{matrix} \right]$, find the values of p,q,r and s
It is given that $X=\left[ \begin{matrix} p & q \\ 8 & 5 \\ \end{matrix} \right],Y=\left[ \begin{matrix} 3p & 5q \\ 2q & 7 \\ \end{matrix} \right]$ Now we have to add $2$ given...
If $M=\left[ \begin{matrix} 5 & r \\ p & 7 \\ \end{matrix} \right],N=\left[ \begin{matrix} q & 4 \\ 3 & s \\ \end{matrix} \right]$and $M+N=\left[ \begin{matrix} 9 & 7 \\ 5 & 8 \\ \end{matrix} \right]$, find the values of p,q,r and s
It is given that $M=\left[ \begin{matrix} 5 & r \\ p & 7 \\ \end{matrix} \right],N=\left[ \begin{matrix} q & 4 \\ 3 & s \\ \end{matrix} \right]$ Now we have to add $2$ given...
If $P=\left[ \begin{matrix} 15 & 13 \\ 11 & 12 \\ 10 & 17 \\ \end{matrix} \right]$, Find the transpose of matrix P and if possible, find the sum of the two matrices. If not possible state the reason.
Given matrix is $P=\left[ \begin{matrix} 15 & 13 \\ 11 & 12 \\ 10 & 17 \\ \end{matrix} \right]$ $P=\left[ \begin{matrix} 15 & 11 & 10 \\ 13 & 12 & 17 \\ \end{matrix}...
If matrix $B=\left[ \begin{matrix} 8 & 5 \\ 7 & 2 \\ \end{matrix} \right]$. find (iii) $B-{{B}^{t}}$
Given matrix $B=\left[ \begin{matrix} 8 & 7 \\ 5 & 2 \\ \end{matrix} \right]$ $B-{{B}^{t}}=\left[ \begin{matrix} 8 & 5 \\ 7 & 2 \\ \end{matrix} \right]-\left[ \begin{matrix} 8...
If matrix $B=\left[ \begin{matrix} 8 & 5 \\ 7 & 2 \\ \end{matrix} \right]$. Find (i) ${{B}^{t}}$ (ii) $B+{{B}^{t}}$
Solution- Given matrix $B=\left[ \begin{matrix} 8 & 7 \\ 5 & 2 \\ \end{matrix} \right]$ (i) ${{B}^{t}}=\left[ \begin{matrix} 8 & 7 \\ 5 & 2 \\ \end{matrix} \right]$ (ii)...
If $P=\left[ \begin{matrix} 1 & 9 & 4 \\ 5 & 0 & 3 \\ \end{matrix} \right]$. Find (i) $–P$ (ii) ${{P}^{t}}$
Given matrix P is a rectangular matrix of order$2\times 3$. Then, Transpose of a matrix is done by interchanging its rows with its columns and columns with rows. (i) $-P=\left[ \begin{matrix} -1...
If $P=\left[ \begin{matrix} 8 & 3 \\ 9 & 7 \\ 4 & 3 \\ \end{matrix} \right]$ and $Q=\left[ \begin{matrix} 4 & 7 \\ 5 & 3 \\ 10 & 1 \\ \end{matrix} \right]$ . Find (i) $P+Q$ (ii) $P-Q$
(i) $P+Q=\left[ \begin{matrix} 8+4 & 3+7 \\ 9+5 & 7+3 \\ 4+10 & 3+1 \\ \end{matrix} \right]$ $=\left[ \begin{matrix} 12 & 10 \\ 14 & 10 \\ 10 & 4 \\ \end{matrix}...
If $X=\left[ \begin{matrix} 17 & 5 & 19 \\ 11 & 8 & 13 \\ \end{matrix} \right]$and $Y=\left[ \begin{matrix} 9 & 3 & 7 \\ 1 & 6 & 5 \\ \end{matrix} \right]$ . Find $2X-3Y$
Given, two X and Y matrices are rectangular matrices of $2\times 3$. Then, $2X=\left[ \begin{matrix} 17\times 2 & 5\times 2 & 19\times 2 \\ 11\times 2 & 8\times 2 & 13\times 2 \\...
If $X=\left[ \begin{matrix} 2 & 9 \\ 5 & 7 \\ \end{matrix} \right]$ and $Y=\left[ \begin{matrix} 7 & 3 \\ 4 & 1 \\ \end{matrix} \right]$ . Find (iii) $3X–2Y$
Given, X and Y two matrices are square matrices of $2\times 2$ Then, (iii) $3X=\left[ \begin{matrix} 3\times 2 & 3\times 9 \\ 3\times 5 & 3\times 7 \\ \end{matrix} \right]$ $=\left[...
If $X=\left[ \begin{matrix} 2 & 9 \\ 5 & 7 \\ \end{matrix} \right]$ and $Y=\left[ \begin{matrix} 7 & 3 \\ 4 & 1 \\ \end{matrix} \right]$ . Find (i) $2X+3Y$ (ii) $2X–Y$
Given, X and Y two matrices are square matrices of $2\times 2$ Then, $2X+3Y$ $2X=\left[ \begin{matrix} 2\times 2 & 9\times 2 \\ 5\times 2 & 7\times 2 \\ \end{matrix} \right]$ $=\left[...
If $X=\left[ \begin{matrix} 4 & 7 \\ \end{matrix} \right]$ and $Y=\left[ \begin{matrix} 3 & 1 \\ \end{matrix} \right]$, find: (iii) $2X–3Y$
From the question it is given that, $X={{\left[ \begin{matrix} 4 & 7 \\ \end{matrix} \right]}_{1\times 2}}$ $Y={{\left[ \begin{matrix} 3 & 1 \\ \end{matrix} \right]}_{1\times 2}}$ (iii)...
If $X=\left[ \begin{matrix} 4 & 7 \\ \end{matrix} \right]$ and $Y=\left[ \begin{matrix} 3 & 1 \\ \end{matrix} \right]$, find: (i) $X+2Y$ (ii) $X–Y$
From the question it is given that, $X={{\left[ \begin{matrix} 4 & 7 \\ \end{matrix} \right]}_{1\times 2}}$ $Y={{\left[ \begin{matrix} 3 & 1 \\ \end{matrix} \right]}_{1\times 2}}$ Then,...
If $X=\left[ \begin{matrix} 12 & 15 \\ 11 & 17 \\ \end{matrix} \right]$$Y=\left[ \begin{matrix} 2 & 7 \\ 4 & 9 \\ \end{matrix} \right]$ : find (iii) $X-2Y$
$2Y=\left[ \begin{matrix} 2\times 2 & 7\times 2 \\ 4\times 2 & 9\times 2 \\ \end{matrix} \right]$ $=\left[ \begin{matrix} 4 & 14 \\ 8 & 18 \\ \end{matrix} \right]$ $X-2Y=\left[...
If $X=\left[ \begin{matrix} 12 & 15 \\ 11 & 17 \\ \end{matrix} \right]$$Y=\left[ \begin{matrix} 2 & 7 \\ 4 & 9 \\ \end{matrix} \right]$: find (i) $X+Y$ (ii) $2X+3Y$
Given X and Y matrices are square matrices of $2\times 2$ (i) $X+Y=\left[ \begin{matrix} 12+2 & 15+7 \\ 11+4 & 17+9 \\ \end{matrix} \right]$ $=\left[ \begin{matrix} 14 & 22 \\ 15...
Find the values of p, q, r and s, if $\left[ \begin{matrix} p+3q & 3r+s \\ 2p-q & r-2s \\ \end{matrix} \right]=\left[ \begin{matrix} 5 & 8 \\ 3 & 5 \\ \end{matrix} \right]$
Given matrices, $\left[ \begin{matrix} p+3q & 3r+s \\ 2p-q & r-2s \\ \end{matrix} \right]=\left[ \begin{matrix} 5 & 8 \\ 3 & 5 \\ \end{matrix} \right]$ $p+3q=5$ … (i) $2p–q=3$ …...
Find the values of p and q, if $\left[ \begin{matrix} 3p-q \\ 7 \\ \end{matrix} \right]=\left[ \begin{matrix} 7 \\ p+q \\ \end{matrix} \right]$
Consider the given two matrices, $\left[ \begin{matrix} 3p-q \\ 7 \\ \end{matrix} \right]=\left[ \begin{matrix} 7 \\ p+q \\ \end{matrix} \right]$ Given two matrices pre rectangular matrices of ....
If $\left[ \begin{matrix} 2a+3b & a-b \\ \end{matrix} \right]=\left[ \begin{matrix} 19 & 2 \\ \end{matrix} \right]$. Find the values of a and b.
According to given question, $2a+3b=19$ … (i) $a–b=2$ … (ii) $a=2+b$ Now, substituting the value of a in equation (i) we get, $2(2+b)+3b=19$ $4+2b+3b=19$ $5b=19–4$ $5b=15$ $b=15/5$ $b=3$ So, $a=2+b$...
Classify the following matrices: (v) $\left[ \begin{matrix} 1 & 1 & 3 & 0 \\ 2 & 1 & 8 & 4 \\ 1 & 5 & 5 & 2 \\ \end{matrix} \right]$
Row of the given matrix $=3$ Column of the given matrix $=4$ So, the order of the given matrix is, $3\times 4$. Therefore, the matrix is a rectangular matrix of $3\times 4$
Classify the following matrices: $\left[ \begin{matrix} 8 & 0 & 0 \\ 5 & 2 & 1 \\ \end{matrix} \right]$ (iv) $\left[ \begin{matrix} 1 & 1 \\ 0 & 9 \\ \end{matrix} \right]$
(iii) Row of the given matrix $=2$ Column of the given matrix $=2$ So, order of the given matrix is, $2\times 3$ Hence, the matrix is a rectangular matrix $=2\times 3$ (iv) Row of the given matrix...
Classify the following matrices: (i) $\left[ \begin{matrix} 2 & 1 \\ 0 & 6 \\ 8 & 7 \\ \end{matrix} \right]$ (ii) $\left[ \begin{matrix} 7 & 0 \\ \end{matrix} \right]$
(i) Row of the given matrix $=3$ Column of the given matrix $=2$ So, order of the given matrix is, $3\times 2$. Hence, the matrix is a rectangular matrix $=3\times 2$. (ii) Row of the given matrix...