Quiz questions for Matrix terminology and notation

True or false?

1. By convention, we consider [0.1 0.3] and to be the same.

2. The matrix has dimensions 2 × 3.

3. The matrices are equal, since they differ in the last column
only, which is zero .

4. The 2, 1 entry of is 0.

5. The matrix is an identity matrix.

6. Suppose we know that the second unit vector (or standard basis vector).
Then we can conclude a = 0.

Quiz questions for §2, Matrix operations .

1. The transpose of the matrix is

(e) not defined
(f) none of the above

(d) not defined
(e) none of the above

3. If , then the product RQ is

(a) the scalar (or 1 × 1 matrix) −2

(b) the matrix

(c) not defined
(d) none of the above

4. If A and B are 3 × 3 matrices, then AB ≠ BA.

False. We usually do not have AB = BA, but there are cases when we do have
AB = BA. One example: take A = B = I.

5. Let Then:

(a) A is singular
(b) A⁻¹ = A^T

(e) none of the above

6. Suppose A and B are 5 × 5 matrices. What is (A + B)^2 − (A − B)^2?

(a) this expression doesn ’t make sense
(b) 4AB
(c) 2AB + 2BA
(d) none of the above

Quiz questions for §3, Linear equations and matrices.

1. Which of the following are linear functions ? Here y = f(x), where x is a 2-vector, and
y is a 2-vector.

(a) Both I and II.
(b) I but not II.
(c) II but not I.
(d) Neither is linear.

2. Which of the following are linear functions ? Here y = f(x), where x is a 3-vector, and
y is a 2-vector.

(a) Both I and II.
(b) I but not II.
(c) II but not I.
(d) Neither is linear.

3. The set of linear equations

can be represented as Ax = b, for which of the following A, b?

(a) Both I and II.
(b) I but not II.
(c) II but not I.
(d) Neither.

4. Which of the following matrix expressions gives the values of three numbers x ₁, x₂,
and x₃, that satisfy the following:

• The average of the first two numbers is 1.
• The average of the last two numbers is 3.
• The average of all three numbers is 2.

We define

5. Solving a set of 100 linear equations in 100 variables

(a) is easily done by hand
(b) is a dangerous task that should be done by certified professionals only
(c) can be done is less than a second on a small PC
(d) is a problem that rarely comes up in practical situations
(e) requires about a minute on a professional workstation computer

6. If the 5-vector x is the solution of the linear equations Ax = b, where A is a 5 × 5
nonsingular matrix, and y is the solution of the linear equations Ay = 2b, what can
you say about x and y?

(a) y = x/2
(b) y = 2x
(c) nothing, because the relation between x and y is complicated
(d) x = y