The adjoint of the matrix N = begin{bmatrix} | vedclass

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

Question

(A) To find the adjoint of matrix $N$,we calculate the cofactor matrix $C$ and then take its transpose $C^T$.The matrix is $N = \begin{bmatrix} -4 & -

Vedclass · Accepted Answer

$N$

Vedclass · Answer

(A) To find the adjoint of matrix $N$,we calculate the cofactor matrix $C$ and then take its transpose $C^T$.The matrix is $N = \begin{bmatrix} -4 & -3 & -3 \ 1 & 0 & 1 \ 4 & 4 & 3 \end{bmatrix}$.The cofactors are calculated as follows:$c_{11} = +((0)(3) - (1)(4)) = -4$$c_{12} = -((1)(3) - (1)(4)) = -(-1) = 1$$c_{13} = +((1)(4) - (0)(4)) = 4$$c_{21} = -((-3)(3) - (-3)(4)) = -(-9 + 12) = -3$$c_{22} = +((-4)(3) - (-3)(4)) = -12 + 12 = 0$$c_{23} = -((-4)(4) - (-3)(4)) = -(-16 + 12) = 4$$c_{31} = +((-3)(1) - (-3)(0)) = -3$$c_{32} = -((-4)(1) - (-3)(1)) = -(-4 + 3) = 1$$c_{33} = +((-4)(0) - (-3)(1)) = 3$The cofactor matrix is $C = \begin{bmatrix} -4 & 1 & 4 \ -3 & 0 & 4 \ -3 & 1 & 3 \end{bmatrix}$.The adjoint is the transpose of the cofactor matrix:$adj(N) = C^T = \begin{bmatrix} -4 & -3 & -3 \ 1 & 0 & 1 \ 4 & 4 & 3 \end{bmatrix} = N$.

The adjoint of the matrix $N = \begin{bmatrix} -4 & -3 & -3 \\ 1 & 0 & 1 \\ 4 & 4 & 3 \end{bmatrix}$ is

Similar Questions

Find the adjoint of the matrix $A = \left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 3 & 5 \\ -2 & 0 & 1\end{array}\right]$.

The inverse of a symmetric matrix is

The element of the second row and third column in the inverse of $\begin{bmatrix} 1 & 2 & 1 \\ 2 & 1 & 0 \\ -1 & 0 & 1 \end{bmatrix}$ is

Let $A$ be a $3 \times 3$ matrix such that $A^T + 2A = I$. Then $\det(A^{-1})$ is equal to:

$A$ and $B$ are $n$-rowed square matrices such that $AB = O$ and $B$ is non-singular. Then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module