Score for this quiz: 20 out of 20

Question 1

1 / 1 pts

All identity matrices are symmetric.

Correct!

True

False

Question 2

1 / 1 pts

All upper-triangular matrices are symmetric.

True

Correct!

False

Question 3

1 / 1 pts

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

Correct!

True

False

Question 4

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 ℛ5 to another vector in ℛ5.)

True

False

Question 5

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. True

False

Question 6

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

Question 7

1 / 1 pts

What’s the rank of the following matrix?

Correct!

2.0 (with margin: 0.0)

Question 8

0 / 1 pts

What’s the rank of the following matrix? 2.0 (with margin: 0.0)

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

1 / 1 pts

The vector is in the kernel of the matrix .

Correct!

True

False

Question 14

1 / 1 pts

The vector is in the kernel of the matrix .

True

Correct!

False

Question 15

1 / 1 pts

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

Correct!

True

False

Question 16

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?

3.0 (with margin: 0.0)

Question 17

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!