First slide

Introduction to Determinants

Question

If $|\begin{array}{lll} p 3 6 \\ 3 6 p \\ 6 p 3 \end{array}| = |\begin{array}{lll} 2 p 7 \\ p 7 2 \\ 7 2 p \end{array}| = |\begin{array}{ccc} 4 & 5 & p \\ 5 & p & 4 \\ p & 4 & 5 \end{array}| = 0$ , then p 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 (p+ 9) common, we get
$p + 9 = 0 or p = - 9$

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