Determinant

Algebra Level 3

$A = \begin{bmatrix}{2} && {3} && {0} \\ {-8} && {k} && {5} \\ {5} && {-1} && {7}\end{bmatrix}$

If the determinant of matrix $A$ is 267, find $k$ .

1 solution

A Former Brilliant Member
Nov 30, 2016

267 = (2xkx7) + (3x5x5) + (0x-8x-1) – (5xkx0) – (-1x5x2) – (7x-8x3)

267 = 14k + 75 + 0 – 0 – (-10) – (-168)

267 = 14k + 75 + 10 + 168

267 = 14k + 253

267 – 253 = 14k

14 = 14k

1 = k