Find the inverse of the matrix,if it exists: | vedclass

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

Question

(A) Let $A = \left[\begin{array}{cc}1 & -1 \ 2 & 3\end{array}ight]$.First,we find the determinant of $A$:$|A| = (1)(3) - (-1)(2) = 3 + 2 = 5$.Since

Vedclass · Accepted Answer

$A^{-1}=\left[\begin{array}{cc}\frac{3}{5} & \frac{1}{5} \ -\frac{2}{5} & \frac{1}{5}\end{array}ight]$

Vedclass · Answer

(A) Let $A = \left[\begin{array}{cc}1 & -1 \ 2 & 3\end{array}ight]$.First,we find the determinant of $A$:$|A| = (1)(3) - (-1)(2) = 3 + 2 = 5$.Since $|A| 
eq 0$,the inverse $A^{-1}$ exists.We use the formula $A^{-1} = \frac{1}{|A|} 	ext{adj}(A)$.The matrix of cofactors is:$C_{11} = 3, C_{12} = -2, C_{21} = 1, C_{22} = 1$.Thus,$	ext{adj}(A) = \left[\begin{array}{cc}3 & 1 \ -2 & 1\end{array}ight]^T = \left[\begin{array}{cc}3 & -2 \ 1 & 1\end{array}ight]$.Wait,let's re-calculate the adjoint correctly:$C_{11} = 3, C_{12} = -2, C_{21} = -(-1) = 1, C_{22} = 1$.So,$	ext{adj}(A) = \left[\begin{array}{cc}3 & 1 \ -2 & 1\end{array}ight]$.Therefore,$A^{-1} = \frac{1}{5} \left[\begin{array}{cc}3 & 1 \ -2 & 1\end{array}ight] = \left[\begin{array}{cc}\frac{3}{5} & \frac{1}{5} \ -\frac{2}{5} & \frac{1}{5}\end{array}ight]$.

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

Similar Questions

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

Let $A = \begin{bmatrix} \cos \theta & -\sin \theta \\ -\sin \theta & -\cos \theta \end{bmatrix}$,then the inverse of $A$ is

Using elementary transformations,find the inverse of the following matrix,if it exists: $\begin{bmatrix} 1 & 2 & 1 \\ 3 & 2 & 3 \\ 1 & 1 & 2 \end{bmatrix}$

If $A$ is a non-singular matrix such that $(A-2I)(A-3I)=O$, then $\frac{1}{5}A + \frac{6}{5}A^{-1} = $

If $A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 1/2 & -1/2 & 1/2 \\ -4 & 3 & c \\ 5/2 & -3/2 & 1/2 \end{bmatrix}$,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module