Page 182 - 35Linear Algebra
P. 182
182 Determinants
Figure 8.6: “The determinant of a product is the product of determinants.”
Which implies that det(MN) = 0 = det M det N.
Thus we have shown that for any matrices M and N,
det(MN) = det M det N
This result is extremely important; do not forget it!
Alternative proof
Reading homework: problem 4
8.3 Review Problems
Reading Problems 1 , 2 , 3 , 4
Webwork: 2 × 2 Determinant 7
Determinants and invertibility 8, 9, 10, 11
1. Let
m 1 m 1 m 1
1 2 3
2
M = m 2 m 2 m .
1 2 3
m 3 1 m 3 2 m 3 3
182