Linear Algebra Quiz Practice Questions - Linear Algebra

Question 1

Which of the following is NOT a vector norm?

Accepted Answer

D) L0 norm

Answer

A) L1 norm

Answer

B) L2 norm

Answer

C) L∞ norm

Question 2

What is the condition number of the identity matrix?

Accepted Answer

B) 1

Answer

A) 0

Answer

C) Undefined

Answer

D) Infinity

Question 3

What is the result of multiplying a 2x3 matrix by a 3x2 matrix?

Accepted Answer

A) 2x2 matrix

Answer

B) 3x3 matrix

Answer

C) 2x3 matrix

Answer

D) 3x2 matrix

Question 4

Which property must a matrix have to be invertible?

Accepted Answer

D) Both A and B

Answer

A) It must be square

Answer

B) Its determinant must be non-zero

Answer

C) It must be symmetric

Question 5

What is the dot product of vectors [1, 2, 3] and [4, 5, 6]?

Accepted Answer

A) 32

Answer

B) 14

Answer

C) 21

Answer

D) 28

Question 6

Which of the following is NOT a property of a vector space?

Accepted Answer

C) Commutativity of multiplication

Answer

A) Closure under addition

Answer

B) Existence of an additive identity

Answer

D) Distributivity of scalar multiplication over vector addition

Question 7

What is the rank of a matrix?

Accepted Answer

A) The number of non-zero rows in its row echelon form

Answer

B) The number of columns minus the number of rows

Answer

C) The sum of its diagonal elements

Answer

D) The largest eigenvalue

Question 8

Which operation is NOT defined for two vectors of the same dimension?

Accepted Answer

B) Cross product

Answer

A) Dot product

Answer

C) Addition

Answer

D) Subtraction

Question 9

What is the determinant of the identity matrix of size 3x3?

Accepted Answer

B) 1

Answer

A) 0

Answer

C) 3

Answer

D) 9

Question 10

Which of the following matrices is orthogonal?

Accepted Answer

B) [[1, 0], [0, 1]]

Answer

A) [[1, 1], [1, -1]]

Answer

C) [[2, 0], [0, 2]]

Answer

D) [[1, 2], [3, 4]]