GATE 2017 ME (ME2) – Question 38
Matrix $A=\begin{bmatrix}50&70\\70&80\end{bmatrix}$ has eigenvectors $\mathbf x_1=(70,\lambda_1-50)^T$ and $\mathbf x_2=(\lambda_2-80,70)^T$ for eigenvalues $\lambda_1,\lambda_2$. The value of $\mathbf x_1^T\mathbf x_2$ is ______.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0 to 0
Explanation
The matrix is real symmetric and has distinct eigenvalues, so its eigenvectors are orthogonal. Explicitly the product is70(λ2−80)+70(λ1−50)=70(λ1+λ2−130). Their sum equals trace50+80=130, giving **0**.