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Assignment 3

1. Evaluate the determinants of the following matrices.

2. Show that

3. Let A be a matrix defined by where a = [2, 0, −1]. If k is a positive integer, find

where I is the 3 × 3 identity matrix.

4. Let

If det(A) = −7, find

5. If A2 = A, find all possible values of det(A).

6. Find all values of k so that each of the following matrices is invertible.

7. Let

(a) Evaluate the determinant of A by cofactor expansion along the first row.

(b) Evaluate the determinant of A by cofactor expansion along the second column.

(c) Find adj(A).

(d) Find A−1 by using Theorem 2.10.

(e) Find det ((3A)−1 + adj(2A))