• # question_answer The matrix $\left| \begin{matrix} 5 & 10 & 3 \\ -2 & -4 & 6 \\ -1 & -2 & b \\ \end{matrix} \right|$is a singular matrix, if b is equal to: A)  $-3$                                   B)  3                            C)  0                            D)         for any value of bE)  for no value of b

Correct Answer: D

Solution :

The matrix$\left[ \begin{matrix} 5 & 10 & 3 \\ -2 & -4 & 6 \\ -1 & -2 & b \\ \end{matrix} \right]$is singular, if $\left| \begin{matrix} 5 & 10 & 3 \\ -2 & -4 & 6 \\ -1 & -2 & b \\ \end{matrix} \right|=0$ $\Rightarrow$$-1(60+12)+2(30+6)$                                                 $+b(-20+20)=0$ $\Rightarrow$               $-72+72+0b=0$ The given matrix is singular for any value of b.

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