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 March 30th, 2015, 08:24 PM #1 Member   Joined: Jan 2015 From: Colorado Posts: 32 Thanks: 0 Find the matrix A with the given eigenvalue and vectors Given that the matrix A has eigenvalues k= 1 with corresponding eigenvector v{1} = [-1,-1] Given that the matrix A has eigenvalues k2= -1 with corresponding eigenvector v{1} = [2,3] find the 2x2 matirx A So I was looking all over online and it said to multiply [-1,2] [-1,3] by [1,0] [0,1] and the inverse of the previous one but that was wrong, I am not sure where to go from here...
April 1st, 2015, 06:34 PM   #2
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I am puzzled by this. If, as you appear to be saying, you do not know what "eigenvalues" and "eigenvectors" are where did you get this problem?

If you do know what "eigenvalues" and "eigenvectors" are then it is just a matter of using their definition:

Quote:
 Originally Posted by mophiejoe Given that the matrix A has eigenvalues k= 1 with corresponding eigenvector v{1} = [-1,-1]
So $\displaystyle \begin{bmatrix}a & b \\ c & d \end{bmatrix}\begin{bmatrix}-1 \\ -1 \end{bmatrix}= \begin{bmatrix}-1 \\ -1 \end{bmatrix}$
That gives you two equations.

Quote:
 Given that the matrix A has eigenvalues k2= -1 with corresponding eigenvector v{1} = [2,3]
$\displaystyle \begin{bmatrix}a & b \\ c & 2 \end{bmatrix}\begin{bmatrix}2 \\ 3 \end{bmatrix}= \begin{bmatrix}-2 \\ -3 \end{bmatrix}$
That gives you two more equations. Solve those four equations for a, b, c, and d.

Quote:
 find the 2x2 matirx A So I was looking all over online and it said to multiply [-1,2] [-1,3] by [1,0] [0,1] and the inverse of the previous one but that was wrong, I am not sure where to go from here...

Last edited by Country Boy; April 1st, 2015 at 06:39 PM.

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