In matrix equation [A] \{X\}=\{R\}. [A]=[\table 4 , 8 , 4 ; 8 , 16 , -4 ; 4 , -4 , 15],\{X\}=\\begin{array}{c}2 \ 1 \ 4\\end{array} and \{R\}=\\begin{array}{c}32 \ 16 \ 64\\end{array} One of the eigenvalues of matrix [A] is

GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

Question : 16 of 65

Marks: +1, -0

In matrix equation [A]

\{X\}=\{R\}

[A]=[\table 4 , 8 , 4 ; 8 , 16 , -4 ; 4 , -4 , 15],\{X\}=\{\table 2 ; 1 ; 4\}

and

\{R\}=\{\table 32 ; 16 ; 64\}

One of the eigenvalues of matrix [A] is

Solution:

[A] {X} = {R}.
We know

A X=λ X ;

Where

λ

- Eigen Value

[\table 4 , 8 , 4 ; 8 , 16 , -4 ; 4 , -4 , 15]\{\table 2 ; 1 ; 4\}=\{\table 32 ; 16 ; 64\}

[\table 4 , 8 , 4 ; 8 , 16 , -4 ; 4 , -4 , 15]\{\table 2 ; 1 ; 4\}=16\{\table 2 ; 1 ; 4\}

Hence,

λ=16

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