If A = begin{bmatrix} 2 & -2 4 & 3 end{bmatr | vedclass

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

Question

(D) The inverse of a $2 	imes 2$ matrix $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$ is given by $A^{-1} = \frac{1}{|A|} 	ext{adj}(A)$,where $

Vedclass · Accepted Answer

$\frac{1}{14} \begin{bmatrix} 3 & 2 \ -4 & 2 \end{bmatrix}$

Vedclass · Answer

(D) The inverse of a $2 	imes 2$ matrix $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$ is given by $A^{-1} = \frac{1}{|A|} 	ext{adj}(A)$,where $|A| = ad - bc$ and $	ext{adj}(A) = \begin{bmatrix} d & -b \ -c & a \end{bmatrix}$.Given $A = \begin{bmatrix} 2 & -2 \ 4 & 3 \end{bmatrix}$.First,calculate the determinant $|A| = (2)(3) - (-2)(4) = 6 - (-8) = 6 + 8 = 14$.Next,find the adjoint of $A$ by swapping the diagonal elements and changing the signs of the off-diagonal elements:$	ext{adj}(A) = \begin{bmatrix} 3 & 2 \ -4 & 2 \end{bmatrix}$.Therefore,$A^{-1} = \frac{1}{14} \begin{bmatrix} 3 & 2 \ -4 & 2 \end{bmatrix}$.This matches option $D$.

If $A = \begin{bmatrix} 2 & -2 \\ 4 & 3 \end{bmatrix}$,then $A^{-1} = $ . . . . . . .

Similar Questions

The adjoint of $\begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & -3 \\ 2 & -1 & 3 \end{bmatrix}$ is

If $A$ and $B$ are square matrices of the same order and $|B| \neq 0$,then $(B^{-1}AB)^5$ is equal to

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$,show that $A^{2} - 5A + 7I = 0$. Hence,find $A^{-1}$.

If $A = \begin{bmatrix} 1 & 2 & 1 \\ 3 & 1 & 3 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 3 \\ 1 & 2 \\ 1 & 2 \end{bmatrix}$,then $(AB)^{-1} =$

If $A = \begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \end{bmatrix}$,$B = \text{adj}(A)$,and $C = 5A$,then find the value of $\frac{|\text{adj}(B)|}{|C|}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module