Chapter 3

Question 1

Determinant via Cofactor Expansion

Answer 1

1. Select a row/column

Repeats

1. For an element in row/column, eliminate the elements on same row/column as it. This reduces size by 1x1.
2. Find determinant of new 2x2 or continue eliminating.
3. Record result from determinant

$(-1)^{1+1} * (element)*(determinant)$ = result

Add all results - Gives determinant of entire matrix.

Question 2

Determinant change when Add

Answer 2

None

Question 3

Determinant change when multiplication

Answer 3

Scaled by multiplication scalar

Question 4

Determinant change when swap

Answer 4

Sign switch

Question 5

Determinant is the __ of the main diagonal of a triangular matrix

Answer 5

Product

Question 6

Determinant via Row Operation

Answer 6

1. Turn matrix into Lower Triangular matrix using Row Operations. Keep track of SCALE/SWITCH actions
2. Multiply every element in the main diagonal
3. Change the value received according to the row operations used. Switch sign/scale

Question 7

How transpose change determinant

Answer 7

Does not

Question 8

Det(A)^2 = ?

Answer 8

Det(A) * Det(A)

Question 9

Det(C^-1) = ?

Answer 9

Det(C^-1) = 1 / Det(C)