516 CHAPTER 27. DETERMINANTS

27.5 Exercises1. Find the determinants of the following matrices.

(a)

 1 2 33 2 20 9 8

 (The answer is 31.)

(b)

 4 3 21 7 83 −9 3

(The answer is

375.)

(c)

1 2 3 21 3 2 34 1 5 01 2 1 2

, (The answer is

−2.)

2. Find the following determinant by expanding along the first row and second column.∣∣∣∣∣∣∣1 2 12 1 32 1 1

∣∣∣∣∣∣∣3. Find the following determinant by expanding along the first column and third row.∣∣∣∣∣∣∣

1 2 11 0 12 1 1

∣∣∣∣∣∣∣4. Find the following determinant by expanding along the second row and first column.∣∣∣∣∣∣∣

1 2 12 1 32 1 1

∣∣∣∣∣∣∣5. Compute the determinant by cofactor expansion. Pick the easiest row or column to

use. ∣∣∣∣∣∣∣∣∣1 0 0 12 1 1 00 0 0 22 1 3 1

∣∣∣∣∣∣∣∣∣6. Find the determinant using row operations.∣∣∣∣∣∣∣

1 2 12 3 2−4 1 2

∣∣∣∣∣∣∣7. Find the determinant using row operations.∣∣∣∣∣∣∣

2 1 32 4 21 4 −5

∣∣∣∣∣∣∣