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 $[\begin{matrix} 5 \\ - 5 \end{matrix}]$ is an eigenvector of the $2 \times 2$ matrix $A = [\begin{array}{cc} 4 & a \\ - 1 & 1 \end{array}] \dots$ corresponding to the eigenvalue $λ$ , then $a + \hat{λ} = ?$

Answer

Popular Problems

If the column vector [5−5] is an eigenvector of the 2×2 matrix A=[4a−11]⋯ corresponding to the eigenvalue λ, then a+λ^=?

Answer

Popular Problems

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