Given basis B: b_{1}=(1\ 2)^{T} and b_{2}=(2\ 1)^{T} and A:

minikim38 2022-01-29 Answered
Given basis B:b1=(1 2)T and b2=(2 1)T and A:a1=(1 2)T, a2=(2 7)T. Find the transformation matrix T from the basis B into basis A?
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enguinhispi
Answered 2022-01-30 Author has 15 answers
Step 1 The change of basis matrix from basis B to basis A is the matrix of the identity map from (R2,A) to (R2,B) Let TB be the matrix with column vectors b1 and b2: its
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basgrwthej
Answered 2022-01-31 Author has 13 answers
The definition of the transformation matrix is A=TB where A is a vector in the new basis and B the same vector in the old basis. So by taking A and B as the basis vectors, you can see that finding T comes down to finding an expansion of the new basis in terms of the old basis.
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