If A=bmatrixa&c&-1\&0&5\\1&-5&0bmatrix is a skew-symmetric matrix, then the value of 2a-(b+c) is : (A) 0 (B) 1 (C) -10 (D) 10

MathsCBSE Class 12 · Board exam 2024, set 65/5/1 · 1 mark · MCQ

CBSE Class 12 Mathematics 2024: question 2

Set in the CBSE Class 12 board exam of 2024, paper 65/5/1, section A, question 2, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q2 · 1 mark · MCQMatrices

If $A = a b 1 c 0 - 5 - 1 50$ is a skew-symmetric matrix, then the value of $2 a - (b + c)$ is :

(A)0
(B)1
(C) $- 10$
(D)10

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 65/5/1.

Hints

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

Hint 1

What must the diagonal entries of a skew-symmetric matrix be?

Hint 2

Use $a_{12} = - a_{21}$ .

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.

In a skew-symmetric matrix every diagonal entry is 0, so $a = 0$ . Also $a_{ij} = - a_{j i}$ , which gives $b = - c$ and $c = - b$ ; using $a_{13} = - 1$ , $a_{31} = 1$ confirms the pattern.
½ mark
Then $b + c = 0$ , so $2 a - (b + c) = 0 - 0 = 0$ , option (A).
½ mark

Answer: 0, option (A)

Where the marks are

Uses $a = 0$ and $b = - c$ to get 0 (1 mark)

Revise the chapter

Chapter: Matrices (notes, formulas, where marks are lost and every past question)
Topic: Symmetric and Skew-Symmetric Matrices

Practise this chapterBoard-style questions from Matrices, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 65/5/1: every question, by section.

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CBSE Class 12 Mathematics 2024: question 2

Hints

Step-by-step solution

Revise the chapter

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