Problem. Consider the polynomials P1, P2, P3 P₁ defined by P₁(t) = 1+t P₂ (t) = 1-t ps(t) = 2. By inspection, write down a linear dependence relation among the three polynomials. Then find a basis for W = Span({P1, P2, P3}). Is it the case hat W = P₁? Explain your answer.

23. Suppose R* = Span {v1, ..., V4}. Explain why {v1,..., V4} is a basis for R4.

1. Determine if these vectors are linearly independent or linearly dependent. If they are linearly independent show this. If they are linearly dependent, write a nontrivial linear combination (at least some coefficients need to be nonzero) of them being equal to 0. {4.0-6)}

1 4. Consider the vectors v1 , Ú2 , U3 1 -2 1 Are they linearly independent? If not either: (a) Find a linear dependence relation among them. or: (b) Express one of the vectors as a linear combination of the others.

Let A = 4 1 -2 -7 V -6 1, b = [77], and c = [] Select true or false for each statement. 1. The vector c is in the range of T 2. The vector b is in the kernel of T Define T(x) = Ax.