If the column vector left[begin{array}{c}5 -5end{array}right] is an eigenvector of the 2 times 2 matrix A=left[begin{array}{cc}4 & a -1 & 1end{array}right] cdots corresponding to the eigenvalue lambda, then a+hat{lambda}=?

Question

If the column vector left[begin{array}{c}5  -5end{array}right] is an eigenvector of the 2 times 2 matrix A=left[begin{array}{cc}4 & a  -1 & 1end{array}right] cdots corresponding to the eigenvalue lambda, then a+hat{lambda}=?

Accepted Answer

Step:1 ：Solve the equation Av = λv, where v = (begin{bmatrix} 5  -5 end{bmatrix}) and A = (begin{bmatrix} 4 & a  -1 & 1 end{bmatrix})Step:2 ：Substitute the solution a = 2 and λ = 2 into the expression a + λStep:3 ：Calculate the final answer: (boxed{4})

Answer

Step: 1 ：Solve the equation Av = λv, where v = (begin{bmatrix} 5  -5 end{bmatrix}) and A = (begin{bmatrix} 4 & a  -1 & 1 end{bmatrix})Step: 2 ：Substitute the solution a = 2 and λ = 2 into the expression a + λStep: 3 ：Calculate the final answer: (boxed{4})

If the column vector $\left[\begin{array}{c}5 \\ -5\end{array}\right]$ is an eigenvector of the $2 \times 2$ matrix $A=\left[\begin{array}{cc}4 & a \\ -1 & 1\end{array}\right] \cdots$ corresponding to the eigenvalue $\lambda$, then $a+\hat{\lambda}=?$

Answer

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