First slide

Introduction to Determinants

Question

If $|\begin{array}{ccc} 1 & - 3 & 4 \\ - 5 & x + 2 & 2 \\ 4 & 1 & x - 6 \end{array}| = 0$ then $x$ equals

Moderate

A

17, 21
B

0, 19
C

0, 35
D

21, 35

Solution

Using $R_{2} \to R_{2} + 5 R_{1}, R_{3} \to R_{3} - 4 R_{1}$
we get
$\begin{array}{l} |\begin{array}{ccc} 1 & - 3 & 4 \\ 0 & x - 13 & 22 \\ 0 & 13 & x - 22 \end{array}| = 0 \\ \Rightarrow (x - 13) (x - 22) - (13) (22) = 0 \\ \Rightarrow x (x - 35) = 0 \Rightarrow x = 0, 35 \end{array}$

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