If A=left[begin{array}{ccc}1 & -1 & 1 2 & -1 | vedclass

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

Question

(B) The adjoint of a matrix $A$ is the transpose of the cofactor matrix. The cofactor $C_{ij}$ is given by $(-1)^{i+j} M_{ij}$.For the given matrix $A

Vedclass · Accepted Answer

$a=2, b=1$

Vedclass · Answer

(B) The adjoint of a matrix $A$ is the transpose of the cofactor matrix. The cofactor $C_{ij}$ is given by $(-1)^{i+j} M_{ij}$.For the given matrix $A = \left[\begin{array}{ccc}1 & -1 & 1 \ 2 & -1 & 0 \ 3 & 3 & -4\end{array}ight]$,we calculate the cofactors for the second and third rows of the adjoint matrix (which correspond to the second and third columns of the cofactor matrix).Specifically,for the element at position $(2, 3)$ in $\operatorname{adj} A$,we need the cofactor $C_{32}$:$C_{32} = (-1)^{3+2} \begin{vmatrix} 1 & 1 \ 2 & 0 \end{vmatrix} = -1(0 - 2) = 2$. Thus,$a = 2$.For the element at position $(3, 3)$ in $\operatorname{adj} A$,we need the cofactor $C_{33}$:$C_{33} = (-1)^{3+3} \begin{vmatrix} 1 & -1 \ 2 & -1 \end{vmatrix} = 1(-1 - (-2)) = 1$. Thus,$b = 1$.Therefore,$a = 2$ and $b = 1$.

If $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4\end{array}\right]$ and $\operatorname{adj} A=\left[\begin{array}{ccc}4 & -1 & 1 \\ 8 & -7 & a \\ 9 & -6 & b\end{array}\right]$,then find the values of $a$ and $b$.

Similar Questions

If a matrix $A$ is such that $3A^3 + 2A^2 + 5A + I = 0$,then its inverse is

Let $I$ be a unit matrix of order $6$. Let $A = (a_{ij})$ be a square matrix of order $6$ such that $a_{ij} = \begin{cases} 1, & \text{if } i+j=7 \\ 0, & \text{if } i+j \neq 7 \end{cases}$. Then $(A(\text{adj } A) A^{-1}) A^2 = $

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$, then $A^{-1} =$

By using elementary operations,find the inverse of the matrix $A=\left[\begin{array}{rr}1 & 2 \\ 2 & -1\end{array}\right]$.

If every element of a square non-singular matrix $A$ of order $n$ is multiplied by $k$ and the new matrix is denoted by $B$,then how are $|A^{-1}|$ and $|B^{-1}|$ related?

Vedclass Test Series

Exam Paper Generator

Online Exam Module