Let T:\mathbb R^2\to \mathbb R^3 be the linear transformation defined by T(x,y)=(y-x,-3x,-3

erycletrefeebr

erycletrefeebr

Answered question

2022-02-25

Let T:R2R3 be the linear transformation defined by T(x,y)=(yx,3x,3y)
Write a linear equation defining the subspace Im(T)
=0Z
(Write your answer in the form ax+by+cz. For example "2x+3y4z")
So, I somehow learned how to find the image or kernels, but have no idea how to write a linear equation of it. Can someone help me with it? At least please give me an answer to this question I can figure out how to do it.

Answer & Explanation

Brody Buckley

Brody Buckley

Beginner2022-02-26Added 5 answers

Hint
Im(T)=Span{T(1,0),T(0,1)}=Span{(1,3,0),(1,0,3)}.
Therefore,
Im(T)={u(1,3,0)+v(1,0,3)u,vR}.
I let you find the cartesian equation.

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