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Question

If P = 13133244 is the adjoint of a 3x3 matrix A and det(A)=4,then α is equal to


A

4

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B

11

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C

5

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D

0

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Solution

The correct option is B

11


We have,
P = 13133244
First we will look at the determinants of the matrix P. The reason is that the determinant of a matrix and the determinant of it’s adjoint are related.
|P| = 1(12-12) - α (4-6)+3(4-6) = 2α - 6
Given, P = adj(A)
Now the important expression required here is,
|adjA|=|A|n1 (where n is the order of the matrix A).
|P|=|adjA|=|A|2=16 (|adjA|=|A|n1)
2α6=16
α=11.


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