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GATE 2023 MT – Question 54

Engineering Mathematics · Linear algebra and matrices · 2 marks · Numerical answer

If $\begin{vmatrix}x+3&3x+4&4x+5\\-2&-3&-4\\-3&-4&-5\end{vmatrix}=0$, then $x=$ ______ (integer).

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Correct answer: 0 to 0

Explanation

The first-row cofactors are −1, +2, −1.

Thus the determinant is $-(x+3)+2(3x+4)-(4x+5)=x$. Setting it to zero gives $x=\boxed0$.