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 $A(\operatorname{adj} A)=5 I$ where $I$ is the identity matrix of order $3$,then $|\operatorname{adj} A|$ is equal to

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

If $A=\left[\begin{array}{ccc}2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2\end{array}\right]$,verify that $A^{3}-6 A^{2}+9 A-4 I=0$ and hence find $A^{-1}$.

If $P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a matrix $A$ and $\det(A) = 4$,then the value of $\alpha$ is

If $A = \begin{bmatrix} \cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$,then $\operatorname{adj} A = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module