Text: A First Course in Linear Algebra (Beezer)
Chapter: Determinants, Exercise C24 (Page 278)
Q: Doing the computations by hand, find the determinant of the matrix below.
\[\begin{bmatrix} -2 & 3 & -2 \\ -4 & -2 & 1 \\ 2 & 4 & 2 \\ \end{bmatrix}\]
A: The formula for the determinant of a 3x3 matrix below is \(det=a(ei−fh)−b(di−fg)+c(dh−eg)\)
\[\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \\ \end{bmatrix}\]
d_calc = -2 * ((-2 * 2) - (1 * 4)) - 3 * ((-4 * 2) - (1 * 2)) -2 * ((-4 * 4) - (-2 * 2))
d_calc## [1] 70We get 70 from the hand calculation, let’s check with the det() function:
d = det(matrix(c(-2, 3, -2, -4, -2, 1, 2, 4, 2), nrow = 3, byrow = TRUE))
d## [1] 70We also get 70 from the det() function, checks out.