First slide

Introduction to Determinants

Question

$| \begin{matrix} x + y & 0 & 0 \\ 0 & x - y & 0 \\ 0 & 0 & x^{2} + y^{2} \end{matrix} | =$

Easy

A

$x^{4} - y^{4}$
B

$x^{4} + y^{4}$
C

$x^{9} - y^{8}$
D

$x^{6} - y^{6}$

Solution

$| \begin{matrix} x + y & 0 & 0 \\ 0 & x - y & 0 \\ 0 & 0 & x^{2} + y^{2} \end{matrix} | = (x + y) (x - y) (x^{2} + y^{2})$
$= x^{4} - y^{4}$

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