First slide

Introduction to Determinants

Question

The value of the determinant $|\begin{matrix} 1 & a & b + c \\ 1 & b & c + a \\ 1 & c & a + b \end{matrix}|$ is

Easy

A

$a + b + c$
B

${(a + b + c)}^{2}$
C

$0$
D

$1 + a + b + c$

Solution

$Δ = || \begin{matrix} 1 & a & b + c \\ 1 & b & c + a \\ 1 & c & a + b \end{matrix}| = (a + b + c) |\begin{matrix} 1 & 1 & b + c \\ 1 & 1 & c + a \\ 1 & 1 & a + b \end{matrix}| = 0,$ $(∵ C_{1} = C_{2})$

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