Let T be a linear transformation from R^{2}\ \text{into}\ R^{2}

Craig French 2022-02-14 Answered
Let T be a linear transformation from R2 into R2 such that T(1,0)=(1,1) and T(0,1)=(1,1). Find T(6,1) and T(5,1)
T(6,1)=?
T(5,1)=?
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Expert Answer

meldElafellrbo
Answered 2022-02-15 Author has 13 answers
Concept: property of linear transformation from Rn to Rm states that T(v1+v2)=T(v1)+T(v2) where T is linear transformation and v1, v2 are vectors from Rn
T(aV1)=aT(V1) where a is scalar, V1 is vector
given T(1,0)=(1,1)
T(0,1)=(1,1)
T(6,1)=? and T(5,1)=?
T(6,1)=T(6+0,0+1)=T((6,0)+(0,1))
using properties of linear transformation we get
=T(6,0)+T(0,1)
=T(6(1,0))+T(0,1)
=6T(1,0)+T(0,1)
=6(1,1)+(1,1)
=(6,6)+(1,1)
=(61,6+1)=(5,7)
linear transformation of (6,1) is (5,7)
T(5,1)=T(5+0,0+1)=T((5,0)+(0,1))
using properties of linear transformation we get
=T(5,0)+T(0,1)
=T(5(1,0))+T(0,1)
=5T(1,0)+T(0,1)
=5(1,1)+(1,1)
=(5,5)+(1,1)
=(51,5+1)=(6,4)
linear transformation of (-5,1) is (-6,-4)
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