anonymous
  • anonymous
Use counter example to show that the funtion T: R2->R3 given by T(x1, x2) = (x1^2,x2,x1+x2) is not a linear transformation from R2 to R3.
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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ganeshie8
  • ganeshie8
Let \(u=(1,3)\) For \(T(u)\) to be a linear transformation, we must have \(T(2u) = 2T(u)\) simply show that above is not satisfied
ganeshie8
  • ganeshie8
\(T(2u)=T(2*1, 2*3)=T(2,6)=(2^2,6,2+6)=(4,6,8)\) \(2T(u) = 2T(1,3)=2(1^2,3,1+3)=2(1,3,4)=(2,6,8)\) \(T(2u)\ne 2T(u)\) so \(T\) is not a linear transformation
anonymous
  • anonymous
Okay I understand now! Thanks!

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ganeshie8
  • ganeshie8
yw

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