Since we will be using various bases and the coordinate systems they define, let's review how we translate between coordinate systems. a. Suppose that we have a basisB={v1,v2,…,vm}forRm. Explain what we mean by the representation {x}g of a vector x in the coordinate system defined by B. b. If we are given the representation {x}B, how can we recover the vector x? c. If we are given the vector x, how can we find {x}B? d. Suppose that BE is a basis for R^2. If xB=[1−2] find the vector x. e. If x=[2−4] find xB

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Since we will be using various bases and the coordinate systems they define, let&#039;s review how we translate between coordinate systems. a. Suppose that we have a basisB={v1,v2,…,vm}forRm. Explain what we mean by the representation {x}g of a vector x in the coordinate system defined by B. b. If we are given the representation {x}B, how can we recover the vector x? c. If we are given the vector x, how can we find {x}B? d. Suppose that BE is a basis for R^2. If xB=[1−2] find the vector x. e. If x=[2−4] find xB

Laith Petty · Accepted Answer

a) Given B={v1,v2...vm} is a basis for Rm{x}B is the coordinate vector of x Corresponding to the basis B that is of x=c1v1+c2v2+c3v3+...+cmvm than {x}B=[c1c2cm] b) Let {x}B=[c1c2cm] then x=c1v1+c2v2+…+cmvm,ci∈R c) Of x is given and B be a basis for Rm than x can be written as the linear combinations of vectors of B that is x=c1v1+c2v2+...+cmvm,ci∈R then {x}B=[c1c2cm] d) B={=[13],{x}B=[11]} is a basis for R2 {x}B=[1−2] x=1[13]−2[11]=[−11] ∵x=[−11] e) x=[2−4]=4[13]+c2[11]=[c1+c23c1+c2] ∵c1+c2=2,3c1+c2=−4 ∵c1=−3,c2=5 ∵{x}B=[−35]

Since we will be using various bases

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