Linear Algebra Quiz

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Basics of vectors and matrices

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Yaj Kotak

United States

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Linear Algebra Quiz


Froggy Jumps Linear Algebra QuizVersion en ligne Basics of vectors and matrices par 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

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Linear Algebra Quiz

Froggy Jumps

À propos de cette activité

Créé par

Téléchargez la version pour jouer sur papier

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Linear Algebra QuizVersion en ligne

par 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: