The determinant [2 1; 3 4] evaluates to 5 and a general [a b; c d] multiplies out to ad − bc, so this Class 12 sheet drills the two-by-two rule before anything else. The key records 1 and 3/2 for later questions.
Key Takeaways
The determinant [2 1; 3 4] is 5 (Q1).
[a b; c d] has value ad − bc (Q2).
The key records 1 and 3/2 as later answers.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The value of the determinant [2 1; 3 4] is
(a) 5(b) -5(c) 8(d) 11
2.The value of the determinant [a b; c d] is
(a) ad - bc(b) ab - cd(c) ac - bd(d) bc - ad
3.The value of the determinant [1 0; 0 1] is
(a) 0(b) 1(c) 2(d) -1
4.If the determinant [x 2; 3 4] = 0, then the value of x is
(a) 2(b) 3/2(c) 3(d) 4
5.The value of a determinant that has two identical rows is
(a) 1(b) 0(c) -1(d) 2
6.For a singular matrix A, the value of |A| is
(a) 1(b) 0(c) -1(d) 2
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Write the value of the determinant [a b; c d].
8.Evaluate the determinant [3 1; 2 4].
9.State the property of a determinant that has two identical rows.
10.Evaluate the determinant [5 0; 0 5].
11.Write the condition for a 2×2 matrix to be singular.
12.Evaluate the determinant [1 2; 3 4].
13.Find the value of x if the determinant [x 2; 4 8] = 0.
14.Write the determinant of the identity matrix of order 2.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.Evaluate the determinant [2 3; 1 4].
16.Find the value of x such that the matrix [x 1; 2 4] is singular.
17.Evaluate the determinant [3 2; 6 4].
18.If the determinant [2 1; x 3] = 5, find the value of x.
19.Find the value of the determinant [7 0; 0 7].
20.Show that the matrix [2 4; 3 6] is singular.
Answer Key
1. a) 5
2. a) ad - bc
3. b) 1
4. b) 3/2
5. b) 0
6. b) 0
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 value of the determinant [2 1; 3 4]?
5, option (a) in this worksheet (Q1).
How is the determinant [a b; c d] calculated?
ad − bc, option (a) in this worksheet (Q2).
What values are recorded later in the key?
1 and 3/2.
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