Consider the matrix A = \left[\begin{array}{cc}50 & 70 \ 70 & 80 \ ]\end{array} whose eigenvectors corresponding to eigenvalues X_1=\left[\begin{array}{c}70 \ \lambda_1-50]\end{array} and X_2=\left[\begin{array}{c}\lambda_2-80 \ 70]\end{array} respectively. The value of x_{1}^{T}x_{2} is ________.

GATE Mechanical Engineering (ME) 2017 Shift 2 Solved Paper

Question : 38 of 65

Marks: +1, -0

Consider the matrix

A = {[\table 50 , 70 ; 70 , 80 ; ]}

whose eigenvectors corresponding to eigenvalues

X_1={[\table 70 ; λ_1-50]}

and

X_2={[\table λ_2-80 ; 70]}

respectively. The value of

x_{1}^{T}x_{2}

is ________.

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