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

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(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

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$a=2, b=1$

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(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 $b$.

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