First slide

Introduction to Determinants

Question

If $|\begin{array}{lll} x 3 6 \\ 3 6 x \\ 6 x 3 \end{array}| = |\begin{array}{lll} 2 x 7 \\ x 7 2 \\ 7 2 x \end{array}| = |\begin{array}{ccc} 4 & 5 & x \\ 5 & x & 4 \\ x & 4 & 5 \end{array}| = 0$ , then x is equal to

Moderate

A

0
B

-9
C

3
D

none of these

Solution

In each determinant applying $R_{1} \to R_{1} + R_{2} + R_{3}$ and then taking out (x + 9) common, we get
$x + 9 = 0 or x = - 9$

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