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 $A = \left[\begin{array}{ll}3 & 1 \ 5 & 2\end{array}ight]$.First,we find the determinant of $A$:$|A| = (3 	imes 2) - (1 	imes 5) = 6 - 5

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Let $A = \left[\begin{array}{ll}3 & 1 \ 5 & 2\end{array}ight]$.First,we find the determinant of $A$:$|A| = (3 	imes 2) - (1 	imes 5) = 6 - 5 = 1$.Since $|A| 
eq 0$,the inverse $A^{-1}$ exists.The formula for the inverse of a $2 	imes 2$ matrix $\left[\begin{array}{ll}a & b \ c & d\end{array}ight]$ is $\frac{1}{|A|} \left[\begin{array}{cc}d & -b \ -c & a\end{array}ight]$.Applying this to matrix $A$:$A^{-1} = \frac{1}{1} \left[\begin{array}{cc}2 & -1 \ -5 & 3\end{array}ight] = \left[\begin{array}{cc}2 & -1 \ -5 & 3\end{array}ight]$.

Find the inverse of the matrix,if it exists: $\left[\begin{array}{ll}3 & 1 \\ 5 & 2\end{array}\right]$

Similar Questions

If $A^2-A+I=0$, then the inverse of the matrix $A$ is

Consider the following statements:
Statement $I$: If $A$ is a non-singular matrix, then $A^{-1}$ exists.
Statement $II$: If $A$ and $B$ are symmetric matrices of the same order, then $(AB - BA)$ is a skew-symmetric matrix.
Choose the correct option.

For the matrix $A = \begin{bmatrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{bmatrix}$,find $A^{-1}$.

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

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module