If inverse of matrix bmatrix7&-3&-3\\-1&1&0\\-1&0&1bmatrix is the matrix bmatrix1&3&3\\1&λ&3\\1&3&4bmatrix, then value of λ is : (A) -4 (B) 1 (C) 3 (D) 4

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

CBSE Class 12 Mathematics 2024: question 4

Set in the CBSE Class 12 board exam of 2024, paper 65/5/1, section A, question 4, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q4 · 1 mark · MCQMatrices

If inverse of matrix $7 - 1 - 1 - 3 10 - 3 01$ is the matrix $111 3 λ 3 334$ , then value of $λ$ is :

(A) $- 4$
(B)1
(C)3
(D)4

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

Use the fact that $A A^{- 1} = I$ .

Hint 2

Pick the entry of the product that involves $λ$ .

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.

Since $A A^{- 1} = I$ , take the (2,2) entry: row 2 of $A$ is $(- 1, 1, 0)$ and column 2 of $A^{- 1}$ is $(3, λ, 3)$ .
½ mark
This gives $- 3 + λ = 1$ , so $λ = 4$ , option (D).
½ mark

Answer: $λ = 4$ , option (D)

Where the marks are

Equates the (2,2) entry of $A A^{- 1}$ to 1 (1 mark)

Revise the chapter

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

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 4

Hints

Step-by-step solution

Revise the chapter

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