3 linear problems in 30 minutes
danstevel8y
linear.docx1) Consider the linear transformation Ta defined by multiplication on the left by the matrix below
A= 4 -7
-2 8
2 1
Is there a vector Ta(v) = <3,3,6>?
2)Suppose that T: IR3 --> IR2 is a linear transformation with T(e1)= <5,-1>, T(e2)= <2,3>, and T(e3)= <-2,5>. Evaluate T(<4,-1,2>) by linearity, that is: first express <4,-1,2> asa linear combination of standard basic vectors and then apply T.
3) Consider the vector u=<5,1,4> Show that the function IR3-->IR# defined by T(v)=v * u is a linear transforation and find [T]
