If A = begin{bmatrix} 1 & a & 3 1 & 1 & 5 2 | vedclass

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(A) We know that $A 	imes A^{-1} = I$,where $I$ is the identity matrix. Calculating the determinant $|A|$: $|A| = 1(7 - 20) - a(7 - 10) + 3(4 - 2) =

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$2, -1$

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(A) We know that $A 	imes A^{-1} = I$,where $I$ is the identity matrix. Calculating the determinant $|A|$: $|A| = 1(7 - 20) - a(7 - 10) + 3(4 - 2) = -13 + 3a + 6 = 3a - 7$. Using the property $A^{-1} = \frac{1}{|A|} 	ext{adj}(A)$,we look at the element at position $(2, 1)$ of $A^{-1}$,which is $-3$. The cofactor $C_{12}$ of $A$ is $-(1 	imes 7 - 5 	imes 2) = -(7 - 10) = 3$. Since $(A^{-1})_{21} = \frac{C_{12}}{|A|}$,we have $-3 = \frac{3}{3a - 7}$. $-3(3a - 7) = 3 \Rightarrow -9a + 21 = 3 \Rightarrow 9a = 18 \Rightarrow a = 2$. Now,for $b$,which is the element at $(2, 2)$ of $A^{-1}$: $(A^{-1})_{22} = \frac{C_{22}}{|A|}$. The cofactor $C_{22} = (1 	imes 7 - 3 	imes 2) = 7 - 6 = 1$. $b = \frac{1}{3(2) - 7} = \frac{1}{6 - 7} = -1$. Thus,$a = 2$ and $b = -1$.

If $A = \begin{bmatrix} 1 & a & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7 \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 13 & 2 & -7 \\ -3 & b & 2 \\ -2 & 0 & 1 \end{bmatrix}$,then the values of $a$ and $b$ are respectively

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