First slide

System of linear equations

Question

$The equations 2 x + y - 4 z = 0, x - 2 y + 3 z = 0, x - y + z = 0 have$

Moderate

A

unique solution
B

no solution
C

infinitely many solutions
D

none

Solution

$|\begin{matrix} 2 & 1 & - 4 \\ 1 & - 2 & 3 \\ 1 & - 1 & 1 \end{matrix}| = 2 (- 2 + 3) - 1 (1 - 3) - 4 (- 1 + 2) = 2 + 2 - 4 = 0$

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