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concon
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Homework Statement
Let So = {v1,v2,v3,v4} be a basis of the vector space V.
S= {u1,u2,u3,u4} is a set of vectors defined as follows:
u1 = 80v1 + 106v2 + 120v3 +164v4
u2 = 80v1 + 146v2 + 136v3 + 91v4
u3 = 90v1 + 143v2 + 122v3 + 70v4
u4 = 80v1 + 56v2 + 80v3 + 48v4
Find the Transition Matrix A from the basis So to S. That is find PS->So. This is the transition matrix from S coordinates to So coordinates.
Homework Equations
I know that to get from one transition matrix to another transition matrix you can take inverse.
Also, for PS->So I know that means you want to turn So into identity matrix.
I have solved problems like this which small numbers, not equations so I am confused.
The Attempt at a Solution
I think the easiest way to solve this (this might be wrong) is to find PSo->S and then take inverse. because the equations are in terms of So. So does that mean I take inverse of this matrix:
80 106 120 164
80 146 136 91
90 143 122 70
80 56 80 48
OR
80 80 90 80
106 146 143 56
120 136 122 80
164 91 70 48
-Or is this not even the way to approach this problem? Any advice would be greatly appreciated. Thanks in advance.