Worksheets › Class 12 › Determinants
Class 12 Determinants worksheet
CBSE Mathematics. Values, area of a triangle, minors and cofactors, adjoint and inverse, solving equations. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
The value of |−6, 1; 7, 7| is:
- 49
- −35
- −55
- −49
Answer
(d) −49
(−6) × 7 − 1 × 7
- 2.
The value of |5, 4, 3; 5, 3, −1; −4, 5, −3| is:
- 172
- 164
- −167
- 167
Answer
(d) 167
expand along the first row: 5 × (−4) + 4 × (19) + 3 × (37)
- 3.
The area of the triangle with vertices (1, −6), (4, 1), (4, −1) is:
- 3 square units
- 4 square units
- 3/2 square units
- 6 square units
Answer
(a) 3 square units
½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)| = ½ × 6
Section B · short answer
- 4.
Find adj A and A⁻¹ for A = [5, 3; 0, 1].
Answer
adj A = [1, −3; 0, 5]; A⁻¹ = [1/5, −3/5; 0, 1]
|A| = 5; A⁻¹ = (1/|A|) adj A
- 5.
Find the inverse of A = [2, 3, 1; 1, 1, −1; 0, 0, −2].
Answer
A⁻¹ = [−1, 3, −2; 1, −2, 3/2; 0, 0, −1/2]
|A| = 2; adj A = [−2, 6, −4; 2, −4, 3; 0, 0, −1]
Section C · long answer
- 6.
Solve by the matrix method: −2x + y + 4z = −14, 2x − 2y = −2, 3x − y + 4z = −31.
Answer
x = −5, y = −4, z = −5
|A| = 24; adj A = [−8, −8, 8; −8, −20, 8; 4, 1, 2]; X = (1/|A|)(adj A)B
Fresh sheets for your child
In the app, every Determinants sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
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