If {bmatrix} -1 & 2 & b \\ a & 5 & 6 \\ 3 & c & 7 {bmatrix} is a symmetric matrix, then {vmatrix} a & b & c \\ b & c & a \\ c & a & b {vmatrix}=

Correct Answer is : −143-143−143

Correct Answer is : −143-143−143

Test Index

TS EAMCET 19-July-2022 Shift 1 Solved Paper

Section: Mathematics

Question : 4 of 160

Marks: +1, -0

\begin{bmatrix} -1 & 2 & b \\ a & 5 & 6 \\ 3 & c & 7 \end{bmatrix}

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

Solution: 👈: Video Solution

Let

A=\begin{bmatrix} -1 & 2 & b \\ a & 5 & 6 \\ 3 & c & 7 \end{bmatrix}

A

is a symmetric matrix, then

A^{T}=A

\begin{bmatrix} -1 & a & 3 \\ 2 & 5 & c \\ b & 6 & 7 \end{bmatrix}=\begin{bmatrix} -1 & 2 & b \\ a & 5 & 6 \\ 3 & c & 7 \end{bmatrix}

On comparing both the matrices, we get

a=2

b=3

and

c=6

\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}=\begin{vmatrix} 2 & 3 & 6 \\ 3 & 6 & 2 \\ 6 & 2 & 3 \end{vmatrix}

\;=2(18-4)-3(9-12)+6(6-.36)

\;=28+9-180

\;=-143

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