The value of A , if A=bmatrix0&2x-1& x\\1-2x&0&2 x\\- x&-2 x&0bmatrix, where x R^+, is (A) (2x+1)² (B) 0 (C) (2x+1)³ (D) (2x-1)²

MathsCBSE Class 12 · Sample paper, session 2023-24 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2023-24: question 10

From the official CBSE sample question paper for 2023-24, section A, question 10, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q10 · 1 mark · MCQDeterminants

The value of $∣ A ∣$ , if $A = 0 1 - 2 x - x 2 x - 1 0 - 2 x x 2 x 0$ , where $x \in R^{+}$ , is

(A) $(2 x + 1)^{2}$
(B)0
(C) $(2 x + 1)^{3}$
(D) $(2 x - 1)^{2}$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

Open one hint at a time and try again before the next.

Hint 1

Compare $A$ with its transpose.

Hint 2

What is the determinant of a skew-symmetric matrix of odd order?

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Each entry satisfies $a_{j i} = - a_{ij}$ and the diagonal is zero, so $A^{T} = - A$ : $A$ is skew-symmetric.
$∣ A ∣ = ∣ A^{T} ∣ = ∣ - A ∣ = (- 1)^{3} ∣ A ∣$ , so $∣ A ∣ = - ∣ A ∣$ and hence $∣ A ∣ = 0$ : option (B).
1 mark

Answer: 0, option (B)

Where the marks are

Recognises a skew-symmetric matrix of odd order, so $∣ A ∣ = 0$ (1 mark)

Revise the chapter

Chapter: Determinants (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Determinants, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24: every question, by section.

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CBSE Class 12 Mathematics sample paper 2023-24: question 10

Hints

Step-by-step solution

Revise the chapter

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