How do you find the determinant of ((1, 2, 1), (-2, 0, 2), (1, 4, 3))?

1 Answer
Mar 4, 2016

The determinant is 0.

Explanation:

There are several ways to compute the determinant.

On of those is the following formula for 3 times 3 matrix:

For a matrix

A = ((a, b, c), (d, e, f), (g, h, i)),

the determinant can found with

det A = a * e * i + d * h * c + g * b * f

" "- c * e * g - f * h * a - i * b * d.

In your case, this means:

det ((1, 2, 1), (-2, 0, 2), (1, 4, 3))

= 1 * 0 * 3 + (-2) * 4 * 1 + 1 * 2 * 2 - 1 * 0 * 1 - 2 * 4 * 1 - 3 * 2 * (-2)

= 0 - 8 + 4 - 0 - 8 + 12

= 0

By the way, this means that the matrix doesn't have an inverse, and that any linear equations solved with this matrix will not have a unique solution but either infinitely many solutions or none at all.