If {bmatrix} 0 & 2 & a \\ b & 0 & 4 \\ -3 & c & 0 {bmatrix} is a skew-symmetric matrix, then {bmatrix} a & b \\ b & a {bmatrix}{bmatrix} b & c \\ c & b {bmatrix}=

Correct Answer is : [2−8−82]{bmatrix} 2 & -8 \\ -8 & 2 {bmatrix}[2−8−82]

{bmatrix} 0 & 0 \\ 0 & 0 {bmatrix}

{bmatrix} 1 & 0 \\ 0 & 1 {bmatrix}

{bmatrix} 2 & -8 \\ -8 & 2 {bmatrix}

{bmatrix} 2 & 8 \\ 8 & 2 {bmatrix}

Correct Answer is : [2−8−82]{bmatrix} 2 & -8 \\ -8 & 2 {bmatrix}[2−8−82]

Test Index

TS EAMCET 19-July-2022 Shift 1 Solved Paper

Section: Mathematics

Question : 3 of 160

Marks: +1, -0

\begin{bmatrix} 0 & 2 & a \\ b & 0 & 4 \\ -3 & c & 0 \end{bmatrix}

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

Solution: 👈: Video Solution

Let

A = \begin{bmatrix} 0 & 2 & a \\ b & 0 & 4 \\ -3 & c & 0 \end{bmatrix}

A

is a skew-symmetric, then

A^T = -A

\begin{bmatrix} 0 & b & -3 \\ 2 & 0 & c \\ a & 4 & 0 \end{bmatrix} = \begin{bmatrix} 0 & -2 & -a \\ -b & 0 & -4 \\ 3 & -c & 0 \end{bmatrix}

\Rightarrow \;\; b = -2, a = 3 \;\text{ and }\; c = -4

\begin{bmatrix} a & b \\ b & a \end{bmatrix}\begin{bmatrix} b & c \\ c & b \end{bmatrix} = \begin{bmatrix} 3 & -2 \\ -2 & 3 \end{bmatrix}\begin{bmatrix} -2 & -4 \\ -4 & -2 \end{bmatrix}

= \begin{bmatrix} 2 & -8 \\ -8 & 2 \end{bmatrix}

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