The inverse of the matrix begin{bmatrix} 1 & | vedclass

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

Question

(B) Let $A = \begin{bmatrix} 1 & 0 & 0 \ 3 & 3 & 0 \ 5 & 2 & -1 \end{bmatrix}$.First,calculate the determinant $|A| = 1(3(-1) - 0(2)) - 0 + 0 = -3$.

Vedclass · Accepted Answer

$-\frac{1}{3} \begin{bmatrix} -3 & 0 & 0 \ 3 & -1 & 0 \ -9 & -2 & 3 \end{bmatrix}$

Vedclass · Answer

(B) Let $A = \begin{bmatrix} 1 & 0 & 0 \ 3 & 3 & 0 \ 5 & 2 & -1 \end{bmatrix}$.First,calculate the determinant $|A| = 1(3(-1) - 0(2)) - 0 + 0 = -3$.Next,find the matrix of cofactors $C_{ij}$:$C_{11} = +((-1)(3) - 0) = -3$,$C_{12} = -(3(-1) - 0) = 3$,$C_{13} = +(3(2) - 3(5)) = -9$.$C_{21} = -(0(-1) - 0(2)) = 0$,$C_{22} = +(1(-1) - 0(5)) = -1$,$C_{23} = -(1(2) - 0(5)) = -2$.$C_{31} = +(0(0) - 3(0)) = 0$,$C_{32} = -(1(0) - 0(3)) = 0$,$C_{33} = +(1(3) - 0(3)) = 3$.Thus,$	ext{Adj}(A) = \begin{bmatrix} -3 & 0 & 0 \ 3 & -1 & 0 \ -9 & -2 & 3 \end{bmatrix}$.Finally,$A^{-1} = \frac{1}{|A|} 	ext{Adj}(A) = \frac{1}{-3} \begin{bmatrix} -3 & 0 & 0 \ 3 & -1 & 0 \ -9 & -2 & 3 \end{bmatrix}$.

The inverse of the matrix $\begin{bmatrix} 1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & -1 \end{bmatrix}$ is

Similar Questions

If $X$ is a square matrix of order $3 \times 3$ and $\lambda$ is a scalar,then $adj(\lambda X)$ is equal to

If $A = \begin{bmatrix} 1 & 2 & 1 \\ 2 & 1 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 2 \\ 2 & 1 \\ 0 & 1 \end{bmatrix}$,then $(AB)^{-1}$ is

If $A$ is a matrix of order $2$ and $I$ is the identity matrix of order $2$ such that $A^2 - 4A + 3I = 0$,then $(A + 3I)^{-1} =$

If $A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A \cdot \operatorname{adj} A = A^T$,then $5a + b$ is equal to

If $A=\begin{bmatrix} \frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}} \end{bmatrix}$,$B=\begin{bmatrix} 1 & 0 \\ i & 1 \end{bmatrix}$,$i=\sqrt{-1}$,and $Q=A^{T}BA$,then the inverse of the matrix $AQ^{2021}A^{T}$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module