For the matrix A=left[begin{array}{ccc}2 & 0 | vedclass

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

Question

(B) To find the matrix of cofactors,we calculate the cofactor $A_{ij}$ for each element $a_{ij}$ using the formula $A_{ij} = (-1)^{i+j} M_{ij}$,where

Vedclass · Accepted Answer

$\left[\begin{array}{ccc}0 & -8 & 4 \ -1 & 3 & -2 \ 1 & -7 & 2\end{array}ight]$

Vedclass · Answer

(B) To find the matrix of cofactors,we calculate the cofactor $A_{ij}$ for each element $a_{ij}$ using the formula $A_{ij} = (-1)^{i+j} M_{ij}$,where $M_{ij}$ is the minor of the element $a_{ij}$.$A_{11} = (-1)^{1+1} \begin{vmatrix} 1 & 2 \ 1 & 2 \end{vmatrix} = (1)(2-2) = 0$$A_{12} = (-1)^{1+2} \begin{vmatrix} 3 & 2 \ -1 & 2 \end{vmatrix} = (-1)(6 - (-2)) = -8$$A_{13} = (-1)^{1+3} \begin{vmatrix} 3 & 1 \ -1 & 1 \end{vmatrix} = (1)(3 - (-1)) = 4$$A_{21} = (-1)^{2+1} \begin{vmatrix} 0 & -1 \ 1 & 2 \end{vmatrix} = (-1)(0 - (-1)) = -1$$A_{22} = (-1)^{2+2} \begin{vmatrix} 2 & -1 \ -1 & 2 \end{vmatrix} = (1)(4 - 1) = 3$$A_{23} = (-1)^{2+3} \begin{vmatrix} 2 & 0 \ -1 & 1 \end{vmatrix} = (-1)(2 - 0) = -2$$A_{31} = (-1)^{3+1} \begin{vmatrix} 0 & -1 \ 1 & 2 \end{vmatrix} = (1)(0 - (-1)) = 1$$A_{32} = (-1)^{3+2} \begin{vmatrix} 2 & -1 \ 3 & 2 \end{vmatrix} = (-1)(4 - (-3)) = -7$$A_{33} = (-1)^{3+3} \begin{vmatrix} 2 & 0 \ 3 & 1 \end{vmatrix} = (1)(2 - 0) = 2$Thus,the matrix of cofactors is $\left[\begin{array}{ccc}0 & -8 & 4 \ -1 & 3 & -2 \ 1 & -7 & 2\end{array}ight]$.

For the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$,the matrix of cofactors is

Similar Questions

If $A = \begin{bmatrix} \cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$,where $A_{21}, A_{22}, A_{23}$ are cofactors of $a_{21}, a_{22}, a_{23}$ respectively,then the value of $a_{21} A_{21} + a_{22} A_{22} + a_{23} A_{23} = $

Write the minors and cofactors of the elements of the following determinant: $\left|\begin{array}{rr}2 & -4 \\ 0 & 3\end{array}\right|$

If $A = \begin{bmatrix} 1 & 1 & 1 \\ 2 & 1 & -3 \\ -1 & 2 & 3 \end{bmatrix}$,then find the value of $A_{31} + A_{32} + A_{33}$,where $A_{ij}$ denotes the cofactor of the element $a_{ij}$ of matrix $A$.

If $A$ is a $3 \times 3$ matrix and the matrix obtained by replacing the elements of $A$ with their corresponding cofactors is $\begin{bmatrix} 1 & -2 & 1 \\ 4 & -5 & -2 \\ -2 & 4 & 1 \end{bmatrix}$, then a possible value of the determinant of $A$ is

For determinant $A = \begin{vmatrix} 1 & 2 & 13 \\ 3 & 0 & 5 \\ 6 & 7 & 11 \end{vmatrix}$,if $p, q, r$ are co-factors of elements $13, 5$ and $11$ respectively,then $p + 3q + 6r = $ . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module