If {a_{ij}} = frac{1}{2}(3i - 2j) and A = {[{ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the formula for elements of the matrix: ${a_{ij}} = \frac{1}{2}(3i - 2j)$.For a $2 	imes 2$ matrix $A = {[{a_{ij}}]_{2 	imes 2}}$,we calcu

Vedclass · Accepted Answer

$\left[ {\begin{array}{*{20}{c}}{1/2}&{ - 1/2}\2&1\end{array}} ight]$

Vedclass · Answer

(B) Given the formula for elements of the matrix: ${a_{ij}} = \frac{1}{2}(3i - 2j)$.For a $2 	imes 2$ matrix $A = {[{a_{ij}}]_{2 	imes 2}}$,we calculate the elements as follows:For $i=1, j=1$: ${a_{11}} = \frac{1}{2}(3(1) - 2(1)) = \frac{1}{2}(3 - 2) = \frac{1}{2}$.For $i=1, j=2$: ${a_{12}} = \frac{1}{2}(3(1) - 2(2)) = \frac{1}{2}(3 - 4) = -\frac{1}{2}$.For $i=2, j=1$: ${a_{21}} = \frac{1}{2}(3(2) - 2(1)) = \frac{1}{2}(6 - 2) = \frac{4}{2} = 2$.For $i=2, j=2$: ${a_{22}} = \frac{1}{2}(3(2) - 2(2)) = \frac{1}{2}(6 - 4) = \frac{2}{2} = 1$.Thus,the matrix $A$ is given by:$A = \left[ {\begin{array}{*{20}{c}}{{a_{11}}}&{{a_{12}}}\{{a_{21}}}&{{a_{22}}}\end{array}} ight] = \left[ {\begin{array}{*{20}{c}}{1/2}&{-1/2}\2&1\end{array}} ight]$.

If ${a_{ij}} = \frac{1}{2}(3i - 2j)$ and $A = {[{a_{ij}}]_{2 \times 2}}$,then $A$ is equal to

Similar Questions

If $A = \begin{bmatrix} 1 & 2 \\ -3 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 0 \\ 2 & 3 \end{bmatrix}$,then:

If $A$ is a $3 \times 4$ matrix and $B$ is a matrix such that $A^{\prime}B$ and $BA^{\prime}$ are both defined,then $B$ is of the type:

The matrix $A^2 + 4A - 5I$,where $I$ is the identity matrix and $A = \begin{bmatrix} 1 & 2 \\ 4 & -3 \end{bmatrix}$,equals:

If $A$ is an $m \times n$ matrix and $B$ is a matrix such that both $AB$ and $BA$ are defined,then the order of $B$ is

If $x\begin{bmatrix} 3 \\ 2 \end{bmatrix} + y\begin{bmatrix} 1 \\ -1 \end{bmatrix} = \begin{bmatrix} 15 \\ 5 \end{bmatrix}$,then the values of $x$ and $y$ are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module