Let A = begin{bmatrix} 3 & -4 1 & -1 end{bma | vedclass

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

Question

(D) Step $1$: Find $A^{-1}$. Given $A = \begin{bmatrix} 3 & -4 \ 1 & -1 \end{bmatrix}$, $\det(A) = (3)(-1) - (-4)(1) = -3 + 4 = 1$. Thus, $A^{-1} = \

Vedclass · Accepted Answer

$(5, 3)$

Vedclass · Answer

(D) Step $1$: Find $A^{-1}$. Given $A = \begin{bmatrix} 3 & -4 \ 1 & -1 \end{bmatrix}$, $\det(A) = (3)(-1) - (-4)(1) = -3 + 4 = 1$. Thus, $A^{-1} = \frac{1}{1} \begin{bmatrix} -1 & 4 \ -1 & 3 \end{bmatrix} = \begin{bmatrix} -1 & 4 \ -1 & 3 \end{bmatrix}$.Step $2$: Calculate $(A^{-1})^2$. $(A^{-1})^2 = \begin{bmatrix} -1 & 4 \ -1 & 3 \end{bmatrix} \begin{bmatrix} -1 & 4 \ -1 & 3 \end{bmatrix} = \begin{bmatrix} (-1)(-1) + (4)(-1) & (-1)(4) + (4)(3) \ (-1)(-1) + (3)(-1) & (-1)(4) + (3)(3) \end{bmatrix} = \begin{bmatrix} -3 & 8 \ -2 & 5 \end{bmatrix}$.Step $3$: Calculate $(A^{-1})^2 + B$. $\begin{bmatrix} -3 & 8 \ -2 & 5 \end{bmatrix} + \begin{bmatrix} 6 & -13 \ 5 & -10 \end{bmatrix} = \begin{bmatrix} 3 & -5 \ 3 & -5 \end{bmatrix}$.Step $4$: Solve the system $\begin{bmatrix} 3 & -5 \ 3 & -5 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 0 \ 0 \end{bmatrix}$. This implies $3x - 5y = 0$, or $3x = 5y$. Among the options, only $(5, 3)$ satisfies $3(5) = 5(3)$, i.e., $15 = 15$.

Similar Questions

If $A$ is a non-singular matrix and $(A+I)(A-I)=0$,then $A+A^{-1} = \dots$

Using elementary transformations,find the inverse of the following matrix,if it exists: $A = \begin{bmatrix} -1 & 2 \\ -3 & 5 \end{bmatrix}$

If $A$ is a non-singular matrix, then $\operatorname{Adj}\left(A^{-1}\right)=$

If the determinant of the adjoint of a (real) matrix of order $3$ is $25$,then the determinant of the inverse of the matrix is

Let $A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right]$,$x \in R^{+}$ and $A^4=\left[a_{ij}\right]_2$. If $a_{11}=109$,then $\left(A^4\right)^{-1}=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module