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Question
The matrix \[\begin{bmatrix}5 & 10 & 3 \\ - 2 & - 4 & 6 \\ - 1 & - 2 & b\end{bmatrix}\] is a singular matrix, if the value of b is _____________ .
Options
-3
3
0
non-existent
Solution
non-existent
For any singular matrix, the value of the determinant is 0.
Here,
\[A = \begin{bmatrix}5 & 10 & 3 \\ - 2 & - 4 & 6 \\ - 1 & - 2 & b\end{bmatrix}\]
\[\left| A \right| = 5( - 4b + 12) - 10( - 2b + 6) + 3(4 - 4) = 0\]
\[ \Rightarrow - 20b + 60 + 20b - 12 = 0\]
Hence, b is non-existent.
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