MATH70 final Math70-FinalSolns-Fall07

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Published on 31 Jan 2019
School
Tufts University
Department
Mathematics
Course
MATH-0070
Professor
Note: the last column of
zeros in A-I_3 doesn't
belong.
NOTE: in fall 2018, we did not cover orthogonal matrices,
so you would be expected to just find
P=[v_1 v_2 v_3] and D (the diagonal matrix with diagonal
entries 1, -2,-2 and note that A=PDP^{-1} .
To find an orthogonal matrix, one needs to find an
orthonormal basis of the eigenspace for lambda _1=1 and an
orthonormal basis of the eigenspace for lambda_2=-2 and
that's what they are doing at the bottom of the page and on
the next page.
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