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I was give the fallowing to prove and i would like it know if anyone thinks i did this right lol....

Let [tex] u_1, u_2, ..., u_k [/tex] be vectors in [tex] R^n [/tex] and [tex] A [/tex] be a [tex] m x n [/tex] matrix. Prove that if [tex] v [/tex] is int he span of [tex] u_1, u_2, ..., u_k [/tex] then [tex] Av [/tex] is in the span of [tex] Au_1, Au_2, ..., Au_k [/tex].

this is what i did to prove this...

If [tex] v [/tex] is in the span of the set [tex] S [/tex] which follows [tex] S = {u_1, u_2, ...,u_k}[/tex] then there is set of coeffients that make the following linear combonation of the elements of the set [tex]S[/tex] that follows the linear equation to prove that [tex]v [/tex] is in the span of [tex] S[/tex]...

[tex]c_1 u_1 + c_2 u_2 + ... + c_k u_k = v[/tex]

to show that [tex]Av[/tex] is in the span of [tex]Au_1, Au_2, ..., Au_k [/tex]

thus the fallowing linear equation must be true...[tex]c_1 Au_1 + c_2 Au_2 + ... + c_k Au_k = Av[/tex] factoring matrix [tex] A[/tex] gives [tex] A(c_1 u_1 + c_2 u_2 + ... + c_k u_k) \rightarrow Av[/tex] thus proving Av is in the span of [tex]Au_1, Au_2, ..., Au_k [/tex]

so did i make any mistakes is this crap? let me know please....

FOR ANYONE WHO'S LATEX ISN'T LOADING HERES THE RAW TYPING

I was give the fallowing to prove and i would like it know if anyone thinks i did this right lol....

Let u_1, u_2, ..., u_k be vectors in R^n and A be a m x n matrix. Prove that if v is int he span of u_1, u_2, ..., u_k then Av is in the span of Au_1, Au_2, ..., Au_k .

this is what i did to prove this...

If v is in the span of the set S which follows S = {u_1, u_2, ...,u_k} then there is set of coeffients that make the following linear combonation of the elements of the set S that follows the linear equation to prove that v is in the span of S...

c_1 u_1 + c_2 u_2 + ... + c_k u_k = v

to show that Av is in the span of Au_1, Au_2, ..., Au_k

thus the fallowing linear equation must be true...c_1 Au_1 + c_2 Au_2 + ... + c_k Au_k = Av factoring matrix A gives A(c_1 u_1 + c_2 u_2 + ... + c_k u_k) -> Av thus proving Av is in the span of Au_1, Au_2, ..., Au_k

so did i make any mistakes is this crap? let me know please....

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# Proof Help Spans

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