Given the basis and coordinates, write the vector in terms of the standard basis.
a. B={[1−3],[21]},xB=[2−2]B[82]
b. B=⎩⎨⎧102,3−13,022⎭⎬⎫,xB=−213B428
Given the vector x written in terms of the standard basis, find the coordinate vector of x with respect to B.
a. x=[−2−8],B={[1−3],[21]}[−18−2]
b. x=[2−1],B={[43],[54]}[32]
c. x=13−2,B=⎩⎨⎧032,130,10−3⎭⎬⎫112−4
Use x=13−2,B=⎩⎨⎧032,130,10−3⎭⎬⎫ to compute [Ax]B and AB where A=2960−1−2034.
Aβ=1533−14−3−3679−12[Ax]β−8628
Find the change of basis matrix for the given bases.