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
B
to
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
B
to
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)=[,|]