Linear Algebra Quiz

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Basics of vectors and matrices

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Yaj Kotak

United States

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Froggy Jumps Linear Algebra QuizOnline version Basics of vectors and matrices by Yaj Kotak 1 1. Which set of vectors forms the standard basis for R3? a A) (1,1,1), (0,1,1), (0,0,1) b B) (1,0,0), (0,1,0), (0,0,1) c D) (0,0,0), (1,0,0), (0,1,0) 2 2. A non-standard basis for R2 must satisfy which condition? a A) Vectors must be perpendicular b C) Vectors must be linearly independent c B) Vectors must have length 1 3 3. What is the first step when converting a matrix to row-reduced echelon form (RREF)? a D) Remove all zero rows b A) Make all entries positive c B) Create leading 1s using row operations 4 4. Which condition must be true for a matrix to be in RREF? a A) Every row must contain a nonzero entry b B) All entries above leading 1s are zero c D) The matrix must be square 5 5. The inner product of two vectors is best described as: a B) A scalar measuring similarity b D) A vector perpendicular to both c A) Their cross product 6 6. Two vectors are orthogonal if their inner product is: a C) 0 b A) 1 c B) -1 7 7. Writing a vector as a linear combination of basis vectors is called: a D) Normalization b B) Decomposition c A) Reduction 8 8. Which statement about matrix multiplication is true? a D) Only square matrices can be multiplied b A) AB = BA for all matrices c C) The number of columns of A must equal the number of rows of B 9 9. If A is a 2x3 matrix and B is a 3x4 matrix, what is the size of AB? a A) 2x3 b B) 3x4 c C) 2x4 10 10. A set of vectors spans a vector space if: a A) They are orthogonal b C) Every vector in the space can be written as their linear combination c B) They are all unit vectors

Froggy Jumps

Linear Algebra QuizOnline version

Basics of vectors and matrices

by Yaj Kotak

1. Which set of vectors forms the standard basis for R3?

A) (1,1,1), (0,1,1), (0,0,1)

B) (1,0,0), (0,1,0), (0,0,1)

D) (0,0,0), (1,0,0), (0,1,0)

2. A non-standard basis for R2 must satisfy which condition?

A) Vectors must be perpendicular

C) Vectors must be linearly independent

B) Vectors must have length 1

3. What is the first step when converting a matrix to row-reduced echelon form (RREF)?

D) Remove all zero rows

A) Make all entries positive

B) Create leading 1s using row operations

4. Which condition must be true for a matrix to be in RREF?

A) Every row must contain a nonzero entry

B) All entries above leading 1s are zero

D) The matrix must be square

5. The inner product of two vectors is best described as:

B) A scalar measuring similarity

D) A vector perpendicular to both

A) Their cross product

6. Two vectors are orthogonal if their inner product is:

C) 0

A) 1

B) -1

7. Writing a vector as a linear combination of basis vectors is called:

D) Normalization

B) Decomposition

A) Reduction

8. Which statement about matrix multiplication is true?

D) Only square matrices can be multiplied

A) AB = BA for all matrices

C) The number of columns of A must equal the number of rows of B

9. If A is a 2x3 matrix and B is a 3x4 matrix, what is the size of AB?

A) 2x3

B) 3x4

C) 2x4

10. A set of vectors spans a vector space if:

A) They are orthogonal

C) Every vector in the space can be written as their linear combination

B) They are all unit vectors

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Linear Algebra Quiz

Froggy Jumps

About this activity

Created by

Download the paper version to play

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Linear Algebra QuizOnline version

by Yaj Kotak

1. Which set of vectors forms the standard basis for R3?

2. A non-standard basis for R2 must satisfy which condition?

3. What is the first step when converting a matrix to row-reduced echelon form (RREF)?

4. Which condition must be true for a matrix to be in RREF?

5. The inner product of two vectors is best described as:

6. Two vectors are orthogonal if their inner product is:

7. Writing a vector as a linear combination of basis vectors is called:

8. Which statement about matrix multiplication is true?

9. If A is a 2x3 matrix and B is a 3x4 matrix, what is the size of AB?

10. A set of vectors spans a vector space if:

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