5.2 Determine the given subset of C[-1,1] is also a vector space.

5.3 Express the given vector v as a linear combination of vectors in the set Q

5.4 Is the set Q above a basis for P²? Explain.

Given the set

Find a subset of R that also spans the same space as R.

5.5 What is the dimension of the span of R above?

What is the dimension of the vector space of all 2x2 matrices?

Explain why R is not a basis for the space of all 2x2 matrices.

5.7 Suppose T:P2 to P4 is a linear transformation where T(1)=x⁴, T(x+1)=x², T(3 + x + x²)=1 + x

Find T(2 + x + x² )

5.8 Find T^-1(x⁴ + x + 1)