# ing techniques from Chapter 5, we can show that det(C) = -59. Since theminant of the coefficient matrix C is nonzero, it follows from Theorem 5.7 (the Bigrem, Version 7) in Section 5.2 that our linear system has only the trivial solution.efore V is a linearly independent set and is a basis for P.DAVID Ithe set V could pos-10,VRx211. V- ((1,0, 0, 0, 0, ...), (1,-1, 0, 0, 0, ...)(1,-1, 1, 0,0,.), (1,-1, 1,-1,0,...),. ., VR12. (1, x+ 1, x+x+1, x+ x2+ x+ 1. ). V=PV PVR2For Exercises 13-18, find a basis for the subspace S and determinedim(S).13. S is the subspace of R consisting of matrices with traceequal to zero, (The trace is the sum of the diagonal terms of amatrix.)VRx214. S is the subspace of P2 consisting of polynomials with graphscrossing the origin.15. S is the subspace of R2x2 consisting of matrices with compo-basis for V.nents that add to zero.16. S is the subspace of T(2, 2) consisting of linear transforma-tions T: R R2 such that T (x) = ax for some scalar a.+ 1, V= P17. S is the subspace of T(2, 2) consisting of linear transforma-tions T: RVRx2R such that T(v) = 0 for a specific vector v.

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Asked Nov 22, 2019
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For Problem #12, how do I prove that the set is a basis for V? I think that infinity is the basis, but I'm not sure. This is a Linear Algebra type of question. Here is a picture.

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