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Question

Mathematics Question on Determinants

If [2+x34 1−12 x1−5]\left[\begin{matrix}2+x&3&4\\\ 1&-1&2\\\ x&1&-5\end{matrix}\right] is a singular matrix, then xx is

A

1325\frac{13}{25}

B

−2513-\frac{25}{13}

C

513\frac{5}{13}

D

2513\frac{25}{13}

Answer

−2513-\frac{25}{13}

Explanation

Solution

Since the matrix is singular. ∴∣2+x34 1−12 x1−5∣=0\therefore\quad\left|\begin{matrix}2+x&3&4\\\ 1&-1&2\\\ x&1&-5\end{matrix}\right|=0 ⇒(2+x)(5−2)−3(−5−2x)+4(1+x)=0\Rightarrow\quad\left(2+x\right)\left(5-2\right)-3\left(-5-2x\right)+4\left(1+x\right)=0 ⇒13x=−25⇒x=−2513\Rightarrow\quad13x=-25 \Rightarrow x=-\frac{25}{13}