SATHEE: Matrices and Determinants 3 Question 1

Matrices and Determinants 3 Question 1

1. If $B =$

$[\begin{matrix} 5 & 2 α & 1 \\ 0 & 2 & 1 \\ α & 3 & - 1 \end{matrix}]$ is the inverse of a $3 \times 3$ matrix $A$ , then the sum of all values of $α$ for which $\det (A) + 1 = 0$ , is

(a) 0

(b) -1

(d) 2

(2019 Main, 12 April I)

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Answer:

Correct Answer: 1. (c)

Solution:

Given matrix $B$ is the inverse matrix of $3 \times 3$ matrix $A$ ,

where $B = [\begin{array}{ccc} 5 & 2 α & 1 \\ 0 & 2 & 1 \\ α & 3 & - 1 \end{array}]$

We know that, $\det (A) = \frac{1}{\det (B)} [∵ \det (A^{- 1}) = \frac{1}{\det (A)}]$

Since, $\det (A) + 1 = 0$ (given)

$\begin{aligned} \frac{1}{\det (B)} + 1 = 0 \\ \Rightarrow \det (B) = - 1 \\ \Rightarrow 5 (- 2 - 3) - 2 α (0 - α) + 1 (0 - 2 α) = - 1 \\ \Rightarrow - 25 + 2 α^{2} - 2 α = - 1 \\ \Rightarrow 2 α^{2} - 2 α - 24 = 0 \\ \Rightarrow α^{2} - α - 12 = 0 \\ \Rightarrow (α - 4) (α + 3) = 0 \\ \Rightarrow α = - 3, 4 \end{aligned}$

So, required sum of all values of $α$ is $4 - 3 = 1$

Matrices and Determinants 3 Question 1

1. If $B =$

Answer:

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Matrices and Determinants 3 Question 1

1. If B=

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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1. If $B =$