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

Find the inverse of the matrix,if it exists: $\left[\begin{array}{ccc}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]$

Let $A$ be a $3 \times 3$ matrix such that $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A ))|=81$. If $S =\{ n \in \mathbb{Z} :(|\operatorname{adj}(\operatorname{adj} A)|)^{\frac{(n-1)^2}{2}}=|A|^{(3n^2-5n-4)}\}$,then $\sum_{n \in S}|A^{(n^2+n)}|$ is equal to

If possible,using elementary row transformations,find the inverse of the following matrix:
$\left[\begin{array}{ccc}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]$

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

If $A$ is a matrix of order $3$,such that $A(\operatorname{adj} A) = 10I$,then $|\operatorname{adj} A| = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module