ISRO 2015- Eigen Values [mech]

Question

$\begin{bmatrix} 4 & 1 \\ 1& 4 \end{bmatrix}$

Eigen values of the matrix are:

a) 3,-3

b) -3, -5

c) 3, 5

d) 5 ,0

Answer 1

Easiest way to solve within a second....

Sum of eigen values is the sum of diagonal elements,

4+4=8

Only option c)3,5 satisfies this..

Hence the answer..:)

Comments

This is when options itself have ambiguity like 2,6

1,7

2,6

Etc because all have some equal to 8.

then given steps are helpfull

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Yes true. But we must attempt shortcut first to save time :)

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product of  eigen valve should be equal to the mod of the matrix

Answer 2

Steps to calculate the Eigenvalues:-

1. Write the matrix in the form of "determinant(A - lambda * I)".

2. Find the characteristic equation and put it equal to 0.

3. Find the root of the characteristic equation and the roots are eigenvalues.

Now, in this case, we are getting characteristic equation as:-

x² - 8x + 15 = 0

On solving we will get x = 3,5 which are the eigenvalues of the characteristic equation.

Hence option C) 3,5 is the answer.

Answer 3

sum of diagonal element 4+4=8

eigen value sum should be 8

so ans C correct