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 $A = \left[\begin{array}{cc}3 & -1 \ -4 & 2\end{array}ight]$.First,calculate the determinant of $A$:$|A| = (3)(2) - (-1)(-4) = 6 - 4 = 2$.S

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Let $A = \left[\begin{array}{cc}3 & -1 \ -4 & 2\end{array}ight]$.First,calculate the determinant of $A$:$|A| = (3)(2) - (-1)(-4) = 6 - 4 = 2$.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 $A$:$A^{-1} = \frac{1}{2} \left[\begin{array}{cc}2 & 1 \ 4 & 3\end{array}ight] = \left[\begin{array}{cc}1 & 1/2 \ 2 & 3/2\end{array}ight]$.

Find the inverse of the matrix,if it exists: $\left[\begin{array}{cc}3 & -1 \\ -4 & 2\end{array}\right]$

Similar Questions

Let $I$ be a unit matrix of order $6$. Let $A = (a_{ij})$ be a square matrix of order $6$ such that $a_{ij} = \begin{cases} 1, & \text{if } i+j=7 \\ 0, & \text{if } i+j \neq 7 \end{cases}$. Then $(A(\text{adj } A) A^{-1}) A^2 = $

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

If $A = \left[\begin{array}{cc}1+2 i & i \\ -i & 1-2 i\end{array}\right]$ where $i=\sqrt{-1}$,then $A (\operatorname{adj} A )=\ldots$. (in $I$)

Let $A$ be any $3 \times 3$ invertible matrix. Then which one of the following is not always true?

The inverse of the matrix $\left[\begin{array}{ccc}7 & -3 & -3 \\ -1 & 1 & 0 \\ -1 & 0 & 1\end{array}\right]$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module