- #1

Mr Davis 97

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## Homework Statement

Write down a 3x3 matrix A such that the equation ##\vec{y}'(t) = A \vec{y}(t)## has a basis of solutions ##y_1=(e^{-t},0,0),~~y_2 = (0,e^{2t},e^{2t}),~~y_3 = (0,1,-1)##

## Homework Equations

## The Attempt at a Solution

I was thinking that, it looks like the matrix would have to have eigenvalues -1, 2, 0, with corresponding eignevectors (1,0,0), (0,1,1), and (0,1,-1). However, I am not sure how I would use this information to construct a matrix.

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