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Matrices Practice Problems with Solutions - CBSE Grade 12

CBSE Grade 12 | Math | Matrices
Name: _________________________ Date: _________________________ Score: _______ / 40

The matrix [[1, 2, 3], [4, 5, 6]] has order 2 × 3 and adding [[1, 2], [3, 4]] to [[5, 6], [7, 8]] gives [[6, 8], [10, 12]], so this Class 12 sheet opens with orders and matrix addition. The key also records a 2 × 2 result and a scalar matrix.

Key Takeaways

Section A: Multiple Choice Questions (1 Mark Each)

Choose the correct option for each question.
1. The order of the matrix A = [ [1, 2, 3], [4, 5, 6] ] is:
(a) 2 × 3(b) 3 × 2(c) 6(d) 2 × 2
2. If A = [ [1, 2], [3, 4] ] and B = [ [5, 6], [7, 8] ], then A + B = ?
(a) [ [6, 8], [10, 12] ](b) [ [5, 12], [21, 32] ](c) [ [4, 4], [4, 4] ](d) [ [6, 8], [8, 10] ]
3. The matrix A = [ [2, 0], [0, 2] ] is called a:
(a) Zero matrix(b) Scalar matrix(c) Identity matrix(d) Column matrix
4. If A = [ [1, 2], [3, 4] ], then the determinant |A| of A is:
(a) -2(b) 2(c) 10(d) 6
5. If A is a 2 × 3 matrix and B is a 3 × 2 matrix, then the product AB is of order:
(a) 3 × 3(b) 2 × 2(c) 2 × 3(d) Not defined
6. Which of the following is the identity matrix of order 2?
(a) [ [1, 0], [0, 1] ](b) [ [1, 1], [1, 1] ](c) [ [0, 0], [0, 0] ](d) [ [1, 0], [1, 0] ]

Section B: Short Answer Type Questions (2 Marks Each)

Show all steps clearly.
7. Define a diagonal matrix and give an example.
8. If A = [ [1, 2], [0, 3] ], write the transpose of A.
9. If A is a 2 × 3 matrix and B is a 3 × 2 matrix, is the product AB defined? If yes, write the order of AB.
10. If A = [ [2, 4], [1, 5] ], find the matrix 2A.
11. State the condition under which two matrices are equal.
12. If A = [ [3], [5], [7] ], write the order of A.
13. If A = [ [1, 2], [3, 4] ] and B = [ [0, 1], [1, 0] ], find the product AB.
14. What is the number of elements in a 3 × 3 matrix?

Section C: Numericals & Word Problems (3 Marks Each)

Apply the concepts to solve the problems. Show all working.
15. The sales of two items over two days are given by A = [ [10, 20], [30, 40] ] for the first two days and B = [ [5, 10], [15, 20] ] for the next two days, where rows are days and columns are items. Find the total sales matrix and the total number of units sold over the four days.
16. The cost per unit of two items is given by the row matrix C = [50, 80]. The sales matrix is S = [ [20, 30], [10, 15] ], where rows are items and columns are days. Find the total daily revenue matrix and the total revenue over the two days.
17. The monthly production of two products by two factories is given by P = [ [100, 200], [150, 250] ] and Q = [ [80, 120], [90, 150] ], where rows are factories and columns are products. Find the total production matrix and the total number of units produced by both factories.
18. The number of men and women in three departments is given by D1 = [30, 20], D2 = [40, 25] and D3 = [35, 15], where the first entry is men and the second is women. Write the 3 × 2 matrix D and find the total number of employees.
19. The marks of a student in two subjects in two tests are given by M = [ [80, 85], [70, 75] ], where rows are tests and columns are subjects. Find the total marks scored in each subject over the two tests.
20. A row matrix of unit prices is P = [25, 40] and the quantities bought are Q = [ [10], [5] ]. Find the product PQ and hence the total cost of the purchase.

Answer Key

1. a) 2 × 3
2. a) [ [6, 8], [10, 12] ]
3. b) Scalar matrix
4. a) -2
5. b) 2 × 2
6. a) [ [1, 0], [0, 1] ]
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet

People Also Ask

What is the order of the matrix [[1, 2, 3], [4, 5, 6]]?

2 × 3, option (a) in this worksheet (Q1).

What is [[1, 2], [3, 4]] + [[5, 6], [7, 8]]?

[[6, 8], [10, 12]], option (a) in this worksheet (Q2).

What is the identity matrix of order 2?

[[1, 0], [0, 1]], option (a) in this worksheet (Q6).

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