Elective Mathematics

Question 1

1The inverse of [[2, 1], [1, 1]] is

Medium

A. [[1, −1], [−1, 2]] B. [[2, −1], [−1, 1]] C. [[−1, 1], [1, −2]] D. [[1, 1], [1, 2]]

Question 2

2If det A = 4, then det(2A) for a 2 × 2 matrix A is

Medium

A. 2 B. 8 C. 4 D. 16

Question 3

3Find the determinant of the 3 × 3 diagonal matrix with diagonal entries 1, 2 and 3.

Easy

A. 0 B. 6 C. 3 D. 9

Question 4

4Find the determinant of [[2, 5], [1, 3]].

Easy

A. −1 B. 1 C. 11 D. 6

Question 5

5Use Cramer's rule: x + y = 3, 2x − y = 0. Then x =

Hard

A. 3 B. 2 C. 1 D. 0

Question 6

6A matrix has no inverse if its determinant is

Easy

A. 1 B. −1 C. positive D. 0

Question 7

7Find x if [[x, 2], [3, 4]] is singular.

Easy

A. 1.5 B. −1.5 C. 6 D. 2

Question 8

8The determinant of [[1, 0, 0], [0, 2, 0], [0, 0, 3]] is

Easy

A. 3 B. 5 C. 0 D. 6

Question 9

9Solve using matrices: 2x + y = 5, x + y = 3. Then x =

Easy

A. 1 B. 2 C. 3 D. 4

Question 10

10To solve the system AX = B when A is invertible, you calculate

Easy

A. X = AB B. X = B − A C. X = BA⁻¹ D. X = A⁻¹B