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(Solved): Consider the following bases and coordinate matrix. B={(4,2,-4),(6,-5,-6),(2,-1,8)} B^(')={(3,2,120 ...
Consider the following bases and coordinate matrix.
B={(4,2,-4),(6,-5,-6),(2,-1,8)}
B^(')={(3,2,120),(1,1,60),(2,2,140)}
{(:[vec(x)]_(B^('))=[[1,-1,2]]^(T)):}Use a software program or a graphing utility to find the transition matrix from
Bto
B^('), find the transition matrix from
B^(')to
B, verify that the two transition matrices are inverses of each other, and find the coordinate matrix
[vec(x)]_(B), given the coordinate matrix
[vec(x)]_(B^(')). (For each answer, enter an exact number as an integer, fraction, or decimal.) (a) Find the transition matrix from
Bto
B^(').
P^(-1)=(b) Find the transition matrix from
B^(')to
B.
P=(c) Verify that the two transition matrices are inverses of each other.
PP^(-1)=(d) Find the coordinate matrix
[vec(x)]_(B), given the coordinate matrix
[vec(x)]_(B^(')).
[vec(x)]_(B)=[,|]