Chapter 11 The Determinant Of A Matrix

Question 1

What is a non-singular matrix?

Answer 1

A matrix A is non-singular if AA = A’A = 1.

Question 2

What does it mean if the determinant of a matrix is zero?

Answer 2

If the determinant of a matrix is zero, the matrix is said to be singular.

Question 3

What happens to points if the determinant of a matrix is zero?

Answer 3

All points are mapped to either a straight line or the origin (in two dimensions).

Question 4

What is the relationship between two square matrices N and M of the same order?

Answer 4

If N and M are square matrices of the same order, then (MN) = N’M⁻¹.

Question 5

What is the formula for the determinant of a 2 x 2 matrix?

Answer 5

The determinant of a 2 x 2 matrix M = [a b; c d] is given by det[M] = ad - bc.

Question 6

What does the determinant of a 2 x 2 matrix represent?

Answer 6

The determinant represents the area scale factor of the transformation.

Question 7

How is the determinant of a matrix denoted?

Answer 7

The determinant of M is written as det(M), |M|, det M, or A.

Question 8

What rule should you use for inverse matrices?

Answer 8

Use the product rule for inverse matrices.