Give a correct answer for given question (A) Argue why (1,0,3),(2,3,1),(0,0,1) is a coordinate system ( bases ) for R3 ? (B) Find the coordinates of (7,6,16) relative to the set in part (A)

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Give a correct answer for given question  (A) Argue why (1,0,3),(2,3,1),(0,0,1) is a coordinate system ( bases ) for R3 ?  (B) Find the coordinates of (7,6,16) relative to the set in part (A)

Adnaan Franks · Accepted Answer

Given B={[103],[231],[001]}  By definition, we say that tha vector {v1,v2,...,vn} are linearly dependent if there exists scalars α1,α2,…,αn not all of them zero such that α1v1+α2v2+…+αnvn=0―.  We say that the vectors {v1,v2,...,vn} are linearly independent if α1v1+α2v2+…+αnvn=0― then    The set of vectors {v1,v2,...,vn} is said to be a basis for vector space V if i) set of vectors {v1,v2,...,vn} is linearly independent ii) span {v1,v2,...,vn}=V If B = {v1,v2,...,vn} is a basis in a vector space V than every vector v→∈V can be uniquely expressed as a linear combination of basis vectors b1,b2,…,bn. i.e there exists unique scalsrs α1,α2,…,αn such that, v→=α1b1+,α2b2+…+αnbn. The coordinates of the vector v→ relative to the basis B is the sequence of co-ordinates, i.e. [v]B=(α1,α2,..,αn)   Consider A=[120030311] Applying R3→R3−3R1, we get R3→R3−3 R1, we get A∼[1200300−51]  Applying R3→5R2+3R3, we get ∼[120030003] (because in eacelon form, first, second and third columns have pivot elements)  ∴ The set of vectors {[103],[231],[001]} is linearly independent dim

Give a correct answer for given question (A) Argue why { (1,0,3), (2,3,1), (0,0,1) } is a coordinate system ( bases ) for R^3 ?(B) Find the coordinates of (7, 6, 16) relative to the set in part (A)

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