Score for this quiz: **20** out of 20

**1 / 1 pts**

All identity matrices are symmetric.

**Correct!**

**True**

False

**1 / 1 pts**

All upper-triangular matrices are symmetric.

True

**Correct!**

**False**

**1 / 1 pts**

All square matrices have the same number of rows as columns.

**Correct!**

**True**

False

**1 / 1 pts**

A “linear operator” is just a linear transformation whose domain is the same dimension as its codomain (for example, it maps each vector in ℛ^{5} to another vector in ℛ^{5}.)

**Correct Answer**

**True**

**You Answered**

False

**1 / 1 pts**

If I perform a linear transformation on a 2-dimensional vector *x* by multiplying it on the left by the matrix *A* below (i.e., performing the multiplication *Ax*) the vector will be rotated 90 degrees clockwise.

**Correct Answer**

**True**

**You Answered**

False

**2 / 2 pts**

Let *y* be the vector that the linear transformation maps the vector to. Which of the following is true of *y*? Check all that apply.

**Correct!**

**all of its elements are even**

you can’t even do that operation

it is 3 dimensional

one of its elements is -3

**Correct!**

**it is 2 dimensional**

it has all zeros

it is 9 dimensional

it is 6 dimensional

**1 / 1 pts**

What’s the rank of the following matrix?

**Correct!**

**Correct Answers**

2.0 (with margin: 0.0)

**0 / 1 pts**

What’s the rank of the following matrix?

**You Answered**

**Correct Answers**

2.0 (with margin: 0.0)

**2 / 2 pts**

Which of the following is true of the matrix operation below? (Check all that apply)

the operation can’t be done

**Correct!**

**all its entries are non-zero**

**Correct!**

**it is a 2×2 matrix**

it is a scalar

all its entries are even

it is a 1×2 vector

**Correct!**

**all its entries are positive**

it is a 2×1 vector

**2 / 2 pts**

Which of the following is true of the result of the matrix-vector multiplication below? (check all that apply)

**Correct!**

**all of its entries are positive**

it is a scalar

**Correct!**

**one of its entries is 16**

this operation can’t be done

it is a 3×3 matrix

all of its entries are even

it is a 1×1 matrix

**1 / 1 pts**

If two matrices M and N are the same dimensions (i.e., M and N each have the same number of rows, and also M and N each have the same number of columns), then you can definitely add them together.

**Correct!**

**True**

False

**1 / 1 pts**

If a matrix Q has 13 rows, and p is a vector with 13 elements, you can definitely multiply Q times p.

True

**Correct!**

**False**

**1 / 1 pts**

The vector is in the kernel of the matrix .

**Correct!**

**True**

False

**1 / 1 pts**

The vector is in the kernel of the matrix .

True

**Correct!**

**False**

**1 / 1 pts**

The vector is in the kernel of *every* 4×4 matrix.

**Correct!**

**True**

False

**1 / 1 pts**

If I told you I had a 16×16 matrix with only 13 linearly independent columns, what would its nullity (*i.e.*, the dimension of its kernel) be?

**You Answered**

**Correct Answers**

3.0 (with margin: 0.0)

**1 / 1 pts**

If I told you that my 17×17 matrix J was full-rank, how many linearly independent rows would you know it had?

**Correct!**

**Correct Answers**

17.0 (with margin: 0.0)