If A = begin{bmatrix} 1 & -1 2 & -1 end{bmat | vedclass

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

Question

(B) First,calculate the sum of matrices $A$ and $B$: $A+B = \begin{bmatrix} 1 & -1 \ 2 & -1 \end{bmatrix} + \begin{bmatrix} 1 & 1 \ 4 & -1 \end{bmat

Vedclass · Accepted Answer

$\begin{bmatrix} \frac{1}{2} & 0 \ \frac{3}{2} & -\frac{1}{2} \end{bmatrix}$

Vedclass · Answer

(B) First,calculate the sum of matrices $A$ and $B$: $A+B = \begin{bmatrix} 1 & -1 \ 2 & -1 \end{bmatrix} + \begin{bmatrix} 1 & 1 \ 4 & -1 \end{bmatrix} = \begin{bmatrix} 2 & 0 \ 6 & -2 \end{bmatrix}$ Next,find the determinant of $(A+B)$: $|A+B| = (2)(-2) - (0)(6) = -4 - 0 = -4$ Since $|A+B| 
eq 0$,the inverse exists. For a matrix $M = \begin{bmatrix} a & b \ c & d \end{bmatrix}$,$M^{-1} = \frac{1}{|M|} \begin{bmatrix} d & -b \ -c & a \end{bmatrix}$. Applying this to $A+B$: $(A+B)^{-1} = \frac{1}{-4} \begin{bmatrix} -2 & 0 \ -6 & 2 \end{bmatrix} = \begin{bmatrix} \frac{-2}{-4} & \frac{0}{-4} \ \frac{-6}{-4} & \frac{2}{-4} \end{bmatrix} = \begin{bmatrix} \frac{1}{2} & 0 \ \frac{3}{2} & -\frac{1}{2} \end{bmatrix}$

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

Similar Questions

If $A = \begin{bmatrix} \sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha \end{bmatrix}$ and $A + A^{-1} = I$,then $\alpha =$

Suppose $n > 1$ and $A$ is a non-singular matrix of order $n$ such that $|\operatorname{adj} A| = |\operatorname{adj}(\operatorname{adj} A)|$. Then the matrix whose rank is $n$ is:

If $\operatorname{det}(AB)=(\operatorname{det} A)(\operatorname{det} B)$ and $A$ is a non-singular matrix of order $3 \times 3$,then $\operatorname{det}(\operatorname{adj} A)=$

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

If $X = \begin{bmatrix} -x & -y \\ z & t \end{bmatrix}$,then the transpose of $\text{adj } X$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module