Question

Linear algebra

Answer 1

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Answer 2

a=(-1,2,2), b=(-3,1,0), c=(1,-1) and function \[f:R ^{3\rightarrow}R ^{2}\] is defined as \[f(x,y,z)=(((x,y,z)\times a)b)c +\left| a \right|(x,y)\], \[(x,y,z)\in R ^{3}\].
Prove that function \[f\] is linear transformation, write it's matrix, find rank of that matrix and check if \[f\] is isomorphism.