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5. Find a 2 \times 2 matrix $A$ for which $E_{-4} = \text{span} \left\{ \begin{bmatrix} -3 \\ -1 \end{bmatrix} \right\}$, $E_2 = \text{span} \left\{ \begin{bmatrix} -5 \\ -2 \end{bmatrix} \right\}$, where $E_\lambda$ denotes the eigenspace associated with the eigenvalue $\lambda$.

          5. Find a 2 \times 2 matrix $A$ for which
$E_{-4} = \text{span} \left\{ \begin{bmatrix} -3 \\ -1 \end{bmatrix} \right\}$, $E_2 = \text{span} \left\{ \begin{bmatrix} -5 \\ -2 \end{bmatrix} \right\}$,
where $E_\lambda$ denotes the eigenspace associated with the eigenvalue $\lambda$.

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5. Find a 2 ×2 matrix A for which
E-4 = span{
< b m a t r i x >
}, E2 = span{
< b m a t r i x >
},
where Eλ denotes the eigenspace associated with the eigenvalue λ.

Added by Daniel W.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Sri K

02/20/2023

Step 1

In other words, Eig(λ) = {v | Av = λv}. Show more…

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5. Find a 2x2 matrix A for which Eig(A) = span{[1, 0]} and Eig(2A) = span{[0, 1]}, where Eig denotes the eigenspace associated with the eigenvalue A.

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