Given that the matrix A has eigenvalue λ1 = 8 with corresponding eigenvector v1 = < b m a t

Step 1: Write the eigenvectors as columns of a matrix V. V = [[1, -2], [2, -3]]

Question

Given that the matrix A has eigenvalue $\lambda_1 = 8$ with corresponding eigenvector $v_1 = \begin{bmatrix} 1 \\ 2 \end{bmatrix}$ and eigenvalue $\lambda_2 = 7$ with corresponding eigenvector $v_2 = \begin{bmatrix} -2 \\ -3 \end{bmatrix}$. Find A. Hint: Treat $Ax = T(x)$ as a linear transformation. A = Note: Input a matrix using square brackets and commas. Put a pair of square brackets around each row and use commas to separate the rows. Then put another pair of square brackets around all the rows. For example, enter $\begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix}$ as "[[1,2], [3,4], [5,6]]".

          Given that the matrix A has eigenvalue $\lambda_1 = 8$ with corresponding eigenvector $v_1 = \begin{bmatrix} 1 \\ 2 \end{bmatrix}$ and eigenvalue $\lambda_2 = 7$ with corresponding eigenvector $v_2 = \begin{bmatrix} -2 \\ -3 \end{bmatrix}$. Find A.
Hint: Treat $Ax = T(x)$ as a linear transformation.
A = 
Note: Input a matrix using square brackets and commas. Put a pair of square brackets around each row and use commas to separate the rows. Then put another pair of square brackets around all the rows. For example, enter
$\begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix}$
as "[[1,2], [3,4], [5,6]]".

Given that the matrix A has eigenvalue λ1 = 8 with corresponding eigenvector v1 =
< b m a t r i x > and eigenvalue λ2 = 7 with corresponding eigenvector v2 =
< b m a t r i x >. Find A.
Hint: Treat Ax = T(x) as a linear transformation.
A =
Note: Input a matrix using square brackets and commas. Put a pair of square brackets around each row and use commas to separate the rows. Then put another pair of square brackets around all the rows. For example, enter
< b m a t r i x >
as "[[1,2], [3,4], [5,6]]".

Added by Nicholas D.

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