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Question

# If P = ⎛⎜⎝1∝3133244⎞⎟⎠ 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 = ⎛⎜⎝1∝3133244⎞⎟⎠ 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|n−1 (where n is the order of the matrix A). |P|=|adjA|=|A|2=16 (|adjA|=|A|n−1) ⇒2α−6=16 ⇒α=11.

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