Matrices

Question 1

If the determinant ≠ 0?

Answer 1

It has a unique solution.
A is non singular.
A^(-1) does exist and is unique.

Question 2

If the determinant = 0?

Answer 2

There is no unique solution.
A is singular.
A^(-1) doesn’t exist.

Question 3

The inverse of a 2x2 matrix?

Answer 3

A^(-1) = (d -b.)

(-c a.)

Question 4

For non-singular matrices A and B, (AB)^(-1) is the same as?

Answer 4

B^(-1)A^(-1)

Question 5

The matrix product NM represents the transformation of?

Answer 5

the transformation M followed by a transformation of N

Question 6

When a shape is transformed by matrix M the ratio of the area of the image shape to the original shape is?

Answer 6

|detM|

Question 7

When the unit square is transformed by the matrix M into a parallelogram, the area of the parallelogram is given by?

Answer 7

|detM| = |ad-bc|

Question 8

If ad-bc > 0 the sense (direction) in which the perimeter of the parallelogram is traced is?

Answer 8

Unaltered by the transformation.

Question 9

If ad-bc < 0 the sense (direction) in which the perimeter of the parallelogram is traced is?

Answer 9

Reversed by the transformation.