If A = begin{bmatrix} 5 & 2 3 & 1 end{bmatri | vedclass

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

Question

(B) To find the inverse of a $2 	imes 2$ matrix $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$,we use the formula $A^{-1} = \frac{1}{|A|} 	ext{a

Vedclass · Accepted Answer

$\begin{bmatrix} -1 & 2 \ 3 & -5 \end{bmatrix}$

Vedclass · Answer

(B) To find the inverse of a $2 	imes 2$ matrix $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$,we use the formula $A^{-1} = \frac{1}{|A|} 	ext{adj}(A)$.Given $A = \begin{bmatrix} 5 & 2 \ 3 & 1 \end{bmatrix}$.First,calculate the determinant $|A| = (5)(1) - (2)(3) = 5 - 6 = -1$.Next,find the adjoint matrix $	ext{adj}(A)$ by swapping the diagonal elements and changing the signs of the off-diagonal elements: $	ext{adj}(A) = \begin{bmatrix} 1 & -2 \ -3 & 5 \end{bmatrix}$.Now,$A^{-1} = \frac{1}{-1} \begin{bmatrix} 1 & -2 \ -3 & 5 \end{bmatrix} = \begin{bmatrix} -1 & 2 \ 3 & -5 \end{bmatrix}$.Thus,the correct option is $B$.

If $A = \begin{bmatrix} 5 & 2 \\ 3 & 1 \end{bmatrix}$,then $A^{-1} = $

Similar Questions

If $A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix}$ and $A^{-1} = \frac{1}{2} \begin{bmatrix} 1 & -1 & 1 \\ -8 & 6 & 2c \\ 5 & -3 & 1 \end{bmatrix}$,then the values of $a$ and $c$ are respectively:

The inverse of the matrix $\begin{bmatrix} 3 & -2 \\ 1 & 4 \end{bmatrix}$ is

If $A = \begin{bmatrix} 3 & 2 \\ 0 & 1 \end{bmatrix}$,then $(A^{-1})^3 = $

If $A$ is a $3 \times 3$ matrix such that $|5 \cdot \text{adj } A| = 5$,then $|A|$ is equal to

Find the inverse of the matrix (if it exists): $\left[\begin{array}{cc}2 & -2 \\ 4 & 3\end{array}\right]$

Vedclass Test Series

Exam Paper Generator

Online Exam Module