GATE Papers >> EEE >> 2019 >> Question No 12

Question No. 12 EEE | GATE 2019

M is a 2 $\times$ 2 matrix with eigenvalues 4 and 9. The eigenvalues of M2 are


Answer : (D) 16 and 81


Solution of Question No 12 of GATE 2019 EEE Paper

Given,

M is a 2 $\times$ 2 matrix with eigen values 4 and 9

$ \therefore $     i.e., $ \mathrm\lambda=4.9 $ [Where $ '\mathrm\lambda' $ represents eigen values of M]

From the properties of eigen values; we have if $ \mathrm\lambda $ is an eigen value of the matrix M then $ \mathrm\lambda^2 $ is an eigen value of the matrix M2.

$ \therefore\mathrm\lambda^2=4^2,9^2=16.81 $ are eigen values of matrix M2.

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