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The 2 × 2 real symmetric matrix A has two distinct eigenvalues, λ1 and λ2. If v1 = (1, 2) is an eigenvector of A corresponding to the eigenvalue λ1, determine an eigenvector corresponding to λ2.

Mathematics
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2 equations 3 unknowns, .. .all the terms of the matrix can be expressed as single variable.
sorry i guess that not easy solving for whole family of matrices, is any info given about the eigen values?

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Other answers:

Nothing any other details..
http://www.math.purdue.edu/~beranger/262/ch5/5-10.pdf ...If you have second check this out and help mee!!!!1
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I got the point.....thanks a lots.....
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