Find the inverse of the matrix A = left[begin | vedclass

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

Question

(A) Given matrix $A = \left[\begin{array}{cc}2 & -3 \ -1 & 2\end{array}ight]$.First,calculate the determinant $|A| = (2)(2) - (-3)(-1) = 4 - 3 = 1$

Vedclass · Accepted Answer

$A^{-1} = \left[\begin{array}{cc}2 & 3 \ 1 & 2\end{array}ight]$

Vedclass · Answer

(A) Given matrix $A = \left[\begin{array}{cc}2 & -3 \ -1 & 2\end{array}ight]$.First,calculate the determinant $|A| = (2)(2) - (-3)(-1) = 4 - 3 = 1$.Since $|A| 
eq 0$,the inverse $A^{-1}$ exists.The formula for the inverse of a $2 	imes 2$ matrix $\left[\begin{array}{cc}a & b \ c & d\end{array}ight]$ is $\frac{1}{ad-bc} \left[\begin{array}{cc}d & -b \ -c & a\end{array}ight]$.Applying this to matrix $A$:$A^{-1} = \frac{1}{1} \left[\begin{array}{cc}2 & 3 \ 1 & 2\end{array}ight] = \left[\begin{array}{cc}2 & 3 \ 1 & 2\end{array}ight]$.

Find the inverse of the matrix $A = \left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$,if it exists.

Similar Questions

If $A$ is a $3 \times 3$ non-singular matrix and if $|A|=3$,then $|(2A)^{-1}|$ is

If $AB = \begin{bmatrix} -6 & 26 \\ -1 & 19 \end{bmatrix}$ and $11B^{-1} = \begin{bmatrix} 5 & -3 \\ 2 & 1 \end{bmatrix}$,then $A = $ . . . . . . .

If $\begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix} \cdot A \cdot \begin{bmatrix} -3 & 2 \\ 5 & -3 \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$,then $A =$

Let $A = \begin{bmatrix} 1 & 2 \\ -1 & 4 \end{bmatrix}$. If $A^{-1} = \alpha I + \beta A$,where $\alpha, \beta \in \mathbb{R}$ and $I$ is a $2 \times 2$ identity matrix,then $4(\alpha - \beta)$ is equal to:

If $A = \begin{bmatrix} 1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4 \end{bmatrix}$,then $(A^2 - 5A)A^{-1} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module