Math 2114SubspacesHomework 5Name:1. LetA=3-101-2-93-3-61503-112-5323228-18-12, which has RREFB=101-203013-702000018000000.Find a basis for the following subspaces:(a) ColA(b) NulA(c) RowA(d) ColB(e) NulB(f) RowB2. LetP4be the set of polynomials of degree at most 4. LetHbe the set:H=p(x)∈P4Z10p(x)dx= 0 andp(0) =p(1) andp0(0) =p0(1)(a) Letp(x) =a4x4+a3x3+a2x2+a1x+a0, translate the equationZ10p(x) = 0 into a linearequation in theai’s. (something likea1+ 2a2+ 4a3= 0)(b) Letp(x) =a4x4+a3x3+a2x2+a1x+a0, translate the equationp(0) =p(1) into a linearequation in theai’s. (something likea1+ 2a2+ 4a3= 0)(c) Letp(x) =a4x4+a3x3+a2x2+a1x+a0, translate the equationp0(0) =p0(1) into a linearequation in theai’s. (something likea1+ 2a2+ 4a3= 0)(d) Consider the three linear equations you found in (a)–(c), write those as a linear system:C~a=~0.
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