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)

Dottie Parra

Dottie Parra

Answered question

2021-01-23

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)

Answer & Explanation

Adnaan Franks

Adnaan Franks

Skilled2021-01-24Added 92 answers

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 vV 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 R3R33R1, we get
R3R33 R1, we get A[120030051]

Applying R35R2+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

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