{adj}{bmatrix} 1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1 {bmatrix} = {bmatrix} 5 & a & -2 \\ 1 & 1 & 0 \\ -2 & -2 & b {bmatrix}, {bmatrix} a & b {bmatrix} is equal to

Correct Answer is : [41]{bmatrix} 4 & 1 {bmatrix}[41]

Correct Answer is : [41]{bmatrix} 4 & 1 {bmatrix}[41]

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EAMCET Engineering 2005 Solved Paper

Section: Mathematics

Question : 99 of 160

Marks: +1, -0

\operatorname{adj}\begin{bmatrix} 1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1 \end{bmatrix} = \begin{bmatrix} 5 & a & -2 \\ 1 & 1 & 0 \\ -2 & -2 & b \end{bmatrix}

\begin{bmatrix} a & b \end{bmatrix}

Solution:

Given that

\;\operatorname{adj}\begin{bmatrix} 1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1 \end{bmatrix} = \begin{bmatrix} 5 & a & -2 \\ 1 & 1 & 0 \\ -2 & -2 & b \end{bmatrix}

. . . (i)

\;\;\text{Cofactor of} \;\begin{bmatrix} 1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1 \end{bmatrix} \text{are}

\; C_{11}=5, C_{12}=1, C_{13}=-2

\; C_{21}=4, C_{22}=1, C_{23}=-2

\; C_{31}=-2, C_{32}=0, C_{33}=1

\; \Rightarrow \begin{bmatrix} 5 & 4 & -2 \\ 1 & 1 & 0 \\ -2 & -2 & 1 \end{bmatrix} = \begin{bmatrix} 5 & a & -2 \\ 1 & 1 & 0 \\ -2 & -2 & b \end{bmatrix}

\;

On comparing the corresponding elements, we get

\; a\; =4, b=1

\therefore \; \begin{bmatrix} a & b \end{bmatrix} \; = \begin{bmatrix} 4 & 1 \end{bmatrix}

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