I'm given a mapping T such that T: R(3) --->R given by T(x,y,z)=2x+3y-4yz i am aware that the yz product is the problem but I'm struggling to explain it in terms of the definition of linear maps ie. T(px+qy) = pT(x)+qT(y).
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T(px+ qy) = pT(x)+qT(y) the variables x and y here in the general formula are different from the parameters of the function T(x,y,z)
u=(x,y,z), v=(a,b,c)
T(pu+qv)=T(p(x,y,z)+q(a,b,c))=T(px+qa,p…
expand and compare it with
pT(u)+qT(v) you'll find them different so all you have to do is conclude
u=(x,y,z), v=(a,b,c)
T(pu+qv)=T(p(x,y,z)+q(a,b,c))=T(px+qa,p…
expand and compare it with
pT(u)+qT(v) you'll find them different so all you have to do is conclude