If f and g are linear transformations are represented by the matrices (0 -4/2 1) and (3 3/-5 -4), what is the image of the point (-1,1) under the composite transformation g o f?

Let T: R? → P2(R) and U : Rª → M2x2 (R) be linear transformations. A student claims U must be invertible because dim(Rª) = dim(M2x2 (R)). If the student is correct, prove their claim. If the student is not correct, explain why and give an example to illustrate. Clearly state whether or not the student is correct as part of your solution.

Suppose T is a linear transformation, and T((−3, −3, —2, —8, 6, 8)) = (−2, 6, −1,0) The matrix T corresponding to this linear transformation is a by matrix.

2. Write down the matrix of the given linear transformation withrespect to the standard bases of the domain and codomain.