Find the determinant of the matrix (4, -3, 5; 1, 0, 4; 0, 3, -1) Answering the following Row 3 & Column 1

Answer 1

Using expansion by minors (Row 3, column 1) (formatting less than ideal:)

4 |0 4| -1 |-3 5|

|3 -1| |3 -1|

4(-12) -1 (3-15) = -48+12 = -36

Answer 2

Sum of products downward diagonals minus sum of products of upward diagonals equals the determinant.

| 4 -3 5 | 4 -3

| 1 0 4 | 1 0

| 0 3 -1 | 0 4 repeated column 1 and 2 to vizualize diagonasl

(4)(0)(-1) + (-3)(4)(0) + (5)(1)(4) - [(0)(0)(5) + (3)(4)(4) + (-1)(1)(-3)]

Can you calculate and answer?