LAHW#09

Due ∞

4.2 Determinant: Properties

• 1.– Let

Establish that f is a linear function of x.

1 2 3

3 7 2

( ) .

5 4 3

f x Det x x x

4.2 Determinants: Properties

• 8.– Compute by cofactor

expansions and by row operations.

2 1 2 5

2 0 4 5

3 1 0 0

1 2 0 0

Det

4.2 Determinant: Properties

• 22.– Consider . Compute the

determinant of this matrix using cofactor expansion.

4 7 8 0 0 5

3 6 9 0 7 3

2 0 0 0 0 0

2 4 2 4 5 2

1 5 3 0 0 0

1 3 4 0 0 0

4.2 Determinant: Properties

• 30.– Let A be an n × n matrix, where n is odd. Establish tha

t if A is skew-symmetric (meaning AT = -A), then Det(A)=0.

4.2 Determinants: Properties

• 36.– Explain why, for two n × n matrices, Det(AB)=

Det(BA). Also, explain why this does not imply that AB = BA.

4.2 Determinants: Properties

• 45.– Let A and B be n × n matrices such that Det(A)

=14 and Det(B)=2. What are the numerical values of Det(AB), Det(BAT), Det(2A), Det(A-1), and Det(B2)?