How do you find the determinant of #((1, 2, 1), (-2, 0, 2), (1, 4, 3))#?
1 Answer
Mar 4, 2016
The determinant is
Explanation:
There are several ways to compute the determinant.
On of those is the following formula for
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.
