First slide

Introduction to Determinants

Question

$|| \begin{matrix} x & y + z & 1 \\ y & x + z & 1 \\ z & x + y & 1 \end{matrix}| =$

Moderate

A

xyz
B

$z + y + z$
C

0
D

$x^{2} + y^{2} + z^{2}$

Solution

$|| \begin{matrix} x & y + z & 1 \\ y & x + z & 1 \\ z & x + y & 1 \end{matrix}| = || \begin{matrix} x + y + z & y + z & 1 \\ x + y + z & x + z & 1 \\ x + y + z & x + y & 1 \end{matrix}| (c_{1} \to c_{1} + c_{2}) = x + y + z || \begin{matrix} 1 & y + z & 1 \\ 1 & x + z & 1 \\ 1 & x + y & 1 \end{matrix}| = 0$

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