Determine if the matrix M is a linear combination of the matrices M_(1),M_(2) and M_(3) :
M=[[2,3],[1,2]], and M_(1)=[[2,2],[1,1]],M_(2)=[[-1,1],[2,1]],M_(3)=[[1,2],[3,1]].
If so, determine scalars c_(1),c_(2),c_(3) such that c_(1)M_(1)+c_(2)M_(2)+c_(3)M_(3)=M.
5. Consider the matrix A=[[1,5],[2,4]] and the vector b=[[3],[5]].
a) Compute the vector A b.
b) Let A_(1) be the first column of A,A_(2) be the second column of A. Compute 3A_(1)+5A_(2).
c) How do the answers from (a) and (b) compare? explain.
6. Let S be a finite set of distinct nonzero vectors in R^(12), and |S|= the number of vectors in the set S. If |S|=14, are the vectors in S linearly independent or linearly dependent? Explain.
7. Assume vectors v_(1),v_(2),v_(3) are nonzero. Explain why the set S={v_(1),v_(2),v_(3)} is linearly dependent if v_(3)=2v_(1)+3v_(2).
4. Determine if the matrix M is a linear combination of the matrices Mi,M and M3
and.
If so, determine scalars c1,C2,C3 such that cMi + c2M2 + c3M3 = M.
5. Consider the matrix A
5
and the vector b
a) Compute the vector Ab. b) Let A, be the first column of A, A2 be the second column of A. Compute 3A1+5A2 c) How do the answers from (a) and (b) compare? explain.
6. Let S be a finite set of distinct nonzero vectors in R12, and |S|=the number of vectors in the set S. If |S| = 14, are the vectors in S linearly independent or linearly dependent? Explain.
7. Assume vectors V1,V2,V3 are nonzero. Explain why the set S = {v1,V2,V3} is linearly dependent if v3=2v1+3v2
