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If $b$ and $c$ are non zero real numbers,
$\mathrm{A}=\left[\begin{array}{lll}1 & b & c \\ b & 2 & 3 \\ c & 3 & 4\end{array}\right]=\left[\begin{array}{ccc}0 & b & c \\ -b & 0 & 2 \\ -c & -2 & 0\end{array}\right]$ and $B$ then $\operatorname{det}(\mathrm{A}+\mathrm{B})=$
Options:
$\mathrm{A}=\left[\begin{array}{lll}1 & b & c \\ b & 2 & 3 \\ c & 3 & 4\end{array}\right]=\left[\begin{array}{ccc}0 & b & c \\ -b & 0 & 2 \\ -c & -2 & 0\end{array}\right]$ and $B$ then $\operatorname{det}(\mathrm{A}+\mathrm{B})=$
Solution:
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Verified Answer
The correct answer is:
$3$
$\mathrm{A}+\mathrm{B}=\left[\begin{array}{lll}1 & b & c \\ b & 2 & 3 \\ c & 3 & 4\end{array}\right]+\left[\begin{array}{ccc}0 & b & c \\ -b & 0 & 2 \\ -c & -2 & 0\end{array}\right]$
$=\left[\begin{array}{ccc}1 & 2 b & 2 c \\ 0 & 2 & 5 \\ 0 & 1 & 4\end{array}\right]$
$\operatorname{det}(A+B)=\left[\begin{array}{ccc}1 & 2 b & 2 c \\ 0 & 2 & 5 \\ 0 & 1 & 4\end{array}\right]$
$=1(4(2)-5(1))=3$
$=\left[\begin{array}{ccc}1 & 2 b & 2 c \\ 0 & 2 & 5 \\ 0 & 1 & 4\end{array}\right]$
$\operatorname{det}(A+B)=\left[\begin{array}{ccc}1 & 2 b & 2 c \\ 0 & 2 & 5 \\ 0 & 1 & 4\end{array}\right]$
$=1(4(2)-5(1))=3$
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