If A = begin{bmatrix} 1 & 2 3 & 4 end{bmatri | vedclass

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

Question

(D) Given $A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$ and $AX = I$.Since $AX = I$,it follows that $X = A^{-1}$.First,find the determinant of $A

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Given $A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$ and $AX = I$.Since $AX = I$,it follows that $X = A^{-1}$.First,find the determinant of $A$: $|A| = (1)(4) - (2)(3) = 4 - 6 = -2$.The inverse of a $2 	imes 2$ matrix $\begin{bmatrix} a & b \ c & d \end{bmatrix}$ is given by $\frac{1}{ad-bc} \begin{bmatrix} d & -b \ -c & a \end{bmatrix}$.Therefore,$A^{-1} = \frac{1}{-2} \begin{bmatrix} 4 & -2 \ -3 & 1 \end{bmatrix}$.$X = \begin{bmatrix} \frac{4}{-2} & \frac{-2}{-2} \ \frac{-3}{-2} & \frac{1}{-2} \end{bmatrix} = \begin{bmatrix} -2 & 1 \ \frac{3}{2} & -\frac{1}{2} \end{bmatrix}$.

If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $X$ is a $2 \times 2$ matrix such that $AX = I$,then $X =$

Similar Questions

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

If a matrix $A$ is such that $3A^3 + 2A^2 + 5A + I = 0$,then its inverse is

If $A = \begin{bmatrix} i & 1 \\ 1 & 0 \end{bmatrix}$ where $i = \sqrt{-1}$ and $B = A^{2029}$,then $B^{-1} =$

If $A = \begin{bmatrix} 4 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}$,then $(A+B)^{-1} = $ . . . . . . .

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module