Question

Suppose 1, 2, … , span . Prove that for any vector , the set , 1, 2, … , also spans .​

Answer 1

Answer:

I don't now this chapter span and vector sorry

Answer 2

Answer:

Let f(x)=vTx. Then w⊥v iff vTw=0 iff f(w)=0 iff kerf=0.

Since the nullspace of a linear operator is a linear space we are finished.

More explicitly, suppose W={w|f(w)=0} then we need to show that if w1,w2∈W then w1+w2∈W and if w∈W and λ is a scalar, then λw∈W.

Since f(w1+w2)=f(w1)+f(w2) and f(λw)=λf(w) we can quickly check these conditions.