In order to be able to multiply the matrices A and B together, A and B must have the same number of rows, and A and B must also have the same number of columns.

Question 1

1 / 1 pts

In order to be able to multiply the matrices A and B together, A and B must have the same number of rows, and A and B must also have the same number of columns.

True

Correct!

False

Question 2

1 / 1 pts

Although not commutative, matrix multiplication is nevertheless associative. (in other words, although AB is not necessarily equal to BA, A(BC) is always equal to (AB)C.)

Correct!

True

False

Question 3

1 / 1 pts

Two square matrices can always be multiplied together.

True

Correct!

False

Question 4

1 / 1 pts

If you multiply any 7×7 matrix Q by the 7×7 identity matrix, the result is guaranteed to be equal to Q itself.

Correct!

True

False

Question 5

1 / 1 pts

If F and G are 9×9 symmetric matrices, then FG (i.e., F times G) is guaranteed to also be a 9×9 symmetric matrix.

True

Correct!

False

Question 6

1 / 1 pts

If M is a matrix, then no matter what M’s dimensions are, I can always perform the operation MM^T (i.e., M times its transpose). Furthermore, the answer to this will be a square matrix.

Correct!

True

False

Question 7

1 / 1 pts

If M is a matrix, then no matter what M’s dimensions are, I can always perform the operation M^TM (i.e., the-transpose-of-M times M). Furthermore, the answer to this will be a square matrix.

Correct!

True

False

Question 8

1 / 1 pts

If a matrix is singular, then it is of full rank.

True

Correct!

False

Question 9

1 / 1 pts

Every matrix has a transpose.

Correct!

True

False

Question 10

1 / 1 pts

Every matrix has an inverse.

True

Correct!

False

Question 11

1 / 1 pts

If M is a matrix, MM^T will always have the same dimensions as M^TM.

True

Correct!

False

Question 12

2 / 2 pts

If I perform the following matrix multiplication, which of the following things are true? (Check all that apply.)

Correct!

The result is a 2×2 matrix.

The result is a 4×4 matrix.

The result is a 4×1 vector.

Correct!

All of the entries in the result are even.

None of the entries in the result are greater than 10.

Correct!

The lowest entry of the result is in its bottom row.

The lowest entry of the result is in its left column.

Both entries in the bottom row are greater than both entries in the top row.

Question 13

1 / 1 pts

How many rows are in the matrix that results from the following operation?

Correct!

Correct Answers

6.0 (with margin: 0.0)

Question 14

1 / 1 pts

How many rows are in the matrix that results from the following operation?

Correct!

Correct Answers

1.0 (with margin: 0.0)

Question 15

1 / 1 pts

What is the rank of the matrix that results from the following operation?

Correct!

Correct Answers

1.0 (with margin: 0.0)

Question 16

1 / 1 pts

The inverse of the matrix $\begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}$ is the matrix $\begin{bmatrix} \frac{3}{2} & -2 \\ -\frac{1}{2} & 1 \end{bmatrix}$ .