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Question
A linear transformation maps (5,2) to (1,-1) and (2,1) to (0,-4). Find the matrix associated with this transformation
Hello Zane,
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Not knowing what techniques you have already learned, here is one way to do it.
Lat the matrix of the transformation be
[a b]
[c d]
Then we can set-up two matrix equations (with the info you gave) to obtain
4 equations with 4 unknowns (a, b, c, and d). Then solving the 4 equations:
5a+2b = 1, 5c+2d = -1, 2a+b = 0, 2c+d = -4
gives
a = 1, b = -2, c = 7, d = -18
so that the matrix is
[1 -2 ]
[7 -18]
See the attached image for the two matrix equations that yield the 4 equations.
I hope this helps.
Abe
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Answers by Expert:
Abe Mantell
Expertise
Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience
Over 15 years teaching at the college level.
Organizations belong to
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.
Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook
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