find the standard matrix for the linear operator t defined by the formula T(x,y,z)=(x-2y ,2x+y)

lwfrgin 2021-02-09 Answered
find the standard matrix for the linear operator t defined by the formula T(x,y,z)=(x2y,2x+y)
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gwibdaithq
Answered 2021-02-10 Author has 84 answers
Here the linear transformation is given by T(x,y,z)=(x2y,2x+y). The standard basis of R3isB2={(1,0,0),(0,1,0),(0,0,1)}
T(1,0,0)=(1,2)=1(1,0)+2(0,1)
T(0,1,0)=(2,1)=2(1,0)+1(0,1)
T(0,0,1)=(0,0)=0(1,0)+0(0,1).
Therefore the standard matrix of T is [T][B2,B3]=[1,2,2,1,0,0].
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