In Exercises 5 through 40, find the matrix of the given linear transformation with respect to the given basis. If no basis is specified, use standard basis: for ,
for and for, . For the space of upper triangular matrices, use the basis
unless another basis is given. In each case, determine whether is an isomorphism. If isn’t an isomorphism, find bases of the kernel and image of and thus determine the rank of .
17.from towith respect to the basis .
The function is linear and isomorphism.