**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**

**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

**1 / 1 pts**

Two square matrices can always be multiplied together.

True

**Correct!**

**False**

**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

**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**

**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

**1 / 1 pts**

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

**Correct!**

**True**

False

**1 / 1 pts**

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

True

**Correct!**

**False**

**1 / 1 pts**

Every matrix has a transpose.

**Correct!**

**True**

False

**1 / 1 pts**

Every matrix has an inverse.

True

**Correct!**

**False**

**1 / 1 pts**

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

True

**Correct!**

**False**

**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.

**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)

**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)

**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)

**1 / 1 pts**

The **inverse** of the matrix is the matrix .

**Correct!**

**True**

False

**1 / 1 pts**

The vector is in the kernel/nullspace of the matrix .

**Correct Answer**

**True**

**You Answered**

False

**1 / 1 pts**

The matrix is singular.

**Correct!**

**True**

False

**1 / 1 pts**

The matrix has an inverse.

True

**Correct!**

**False**