Question

Given the matrix

A= a 6 5
a -8 8
7 9 a

find all values of a that make |A|=0. Give your answer as a comma-separated list.

Answer 1

-8 a^2 -72 a + 336 - 6 a^2 + 45 a + 280 = 0
-14 a^2 -27 a + 616 = 0
or
14 a^2 + 27 a - 616 = 0
https://www.mathsisfun.com/quadratic-equation-solver.html
-7.67
+5.74
Check my arithmetic
Here is a matrix determinant calculator:
https://www.symbolab.com/solver/matrix-determinant-calculator/%5Cdet%5Cbegin%7Bpmatrix%7D5.74%20%26%206%20%26%205%20%5C%5C%205.74%20%26%20-8%20%26%208%5C%5C%207%20%269%20%26%205.74%5Cend%7Bpmatrix%7D