Question

Let WW be a subset of a vector space VV. By justifying your answer, determine whether WW is a subspace of VV.

(a) [5 marks] W={(x1,x2,x3,x4):x1x4=0}W={(x1,x2,x3,x4):x1x4=0} and V=R4V=R4.

(b) [5 marks] W={A:|A|≥1}W={A:|A|≥1} and V=M3,3V=M3,3, where |A||A| is the determinant of AA.

(c) [10 marks] W={p(x)=a0+a1x+a2x2+a3x3:a0=a1anda2=a3}W={p(x)=a0+a1x+a2x2+a3x3:a0=a1anda2=a3} and V=P3V=P3.

Answer 1

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