Matrices and Determinants 3 Question 1

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1. If B=021 is the inverse of a 3×3 matrix A, then α31 the sum of all values of α for which det(A)+1=0, is

======= ####1. If B= [52α1021α31] is the inverse of a 3×3 matrix A, then the sum of all values of α for which det(A)+1=0, is

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed

(a) 0

(b) -1

(c) 1

(d) 2

(2019 Main, 12 April I)

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Answer:

Correct Answer: 1. (c)

Solution:

  1. Given matrix B is the inverse matrix of 3×3 matrix A,

where B=[52α1021α31]

We know that, det(A)=1det(B)[det(A1)=1det(A)]

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

1det(B)+1=0det(B)=15(23)2α(0α)+1(02α)=125+2α22α=12α22α24=0α2α12=0(α4)(α+3)=0α=3,4

So, required sum of all values of α is 43=1



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