Matrices and Determinants 2 Question 21

23. Which of the following values of α satisfy the equation

|(1+α)2(1+2α)2(1+3α)2(2+α)2(2+2α)2(2+3α)2(3+α)2(3+2α)2(3+3α)2|=648α ?

(a) -4

(b) 9

(c) -9

(d) 4

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Answer:

Correct Answer: 23. (b,c)

Solution:

  1. Given determinant could be expressed as product of two determinants.

 i.e. |(1+α)2(1+2α)2(1+3α)2(2+α)2(2+2α)2(2+3α)2(3+α)2(3+2α)2(3+3α)2|=648α

|1+2α+α21+4α+4α21+6α+9α24+4α+α24+8α+4α24+12α+9α29+6α+α29+12α+4α29+18α+9α2| 648α

|1αα242αα293αα2||111246149|=648α

α3|111421931||111246149|=648α

8α3=648α

α381α=0α(α281)=0

α=0,±9



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