Module 8 Quiz

Introduction to Matrices

Instructions

This quiz contains 15 multiple choice questions covering all topics in Module 8. You need to score at least 70% (11 out of 15 correct) to pass. Select one answer for each question, then click "Submit Quiz" to see your results.

Question 1

What are the dimensions of matrix A = [1 2 3; 4 5 6]?

3 × 2 2 × 3 6 × 1 3 × 3

Question 2

If A = [3 -2; 1 4] and B = [2 5; -1 3], what is A + B?

[5 3; 0 7] [1 -7; 2 1] [6 -10; -1 12] [5 3; 2 7]

Question 3

If C = [2 -1; 3 0], what is 3C?

[5 2; 6 3] [6 -3; 9 0] [6 -1; 3 0] [2 -3; 9 0]

Question 4

Which pair of matrices can be multiplied to produce matrix AB?

A is 3×2, B is 3×4 A is 3×2, B is 2×4 A is 2×3, B is 4×2 A is 2×2, B is 3×2

Question 5

What is the determinant of [4 3; 2 1]?

-2 2 10 -10

What is the determinant of [2 0; 0 5]?

0 7 10 -10

Question 7

If det(A) = 4 for a 2×2 matrix A, what is det(3A)?

12 16 36 64

Question 8

A matrix is invertible if and only if:

It is a square matrix Its determinant is non-zero All its entries are positive It is a 2×2 matrix

Question 9

What is the inverse of A = [5 2; 2 1]?

[1 -2; -2 5] [1 2; 2 5] [-1 2; 2 -5] [5 -2; -2 1]

Question 10

If A = [3 1; 5 2] and A^-1 = [2 -1; -5 3], what is AA^-1?

[0 0; 0 0] [1 0; 0 1] [1 1; 1 1] [5 0; 0 5]

Question 11

Which matrix is NOT invertible?

[2 3; 4 5] [1 0; 0 1] [2 4; 1 2] [3 -1; 2 5]

Question 12

To solve the matrix equation AX = B for X, you should:

Multiply both sides by A Multiply both sides by A^-1 Divide both sides by A Add A to both sides

Question 13

In Cramer's Rule, to find the value of x in a system AX = B, you calculate:

det(A) / det(A_x) det(A_x) / det(A) det(A) × det(A_x) det(A) + det(A_x)

Question 14

For the 2×2 inverse formula, if A = [a b; c d], then A^-1 equals:

(1/det(A))[a -b; -c d] (1/det(A))[d -b; -c a] (1/det(A))[d b; c a] (1/det(A))[-a b; c -d]

Question 15

Which operation is NOT defined for all pairs of matrices?

Matrix addition Scalar multiplication Matrix multiplication Finding the transpose

Quiz Results

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