(adsbygoogle = window.adsbygoogle || []).push({}); Suppose [itex] X_{1},X_{2},...,X_{N} [/itex] ae vectors in Rn. If [itex] Y = a_{1} X_{1} ... + a_{N} X_{N} [/itex] where ai is not zero, show that

[tex] span{X_{1},...,X{N}} = span{Y,X_{2},...,X_{N}} [/tex]

WELL

[tex] span{X_{1},...,X{N}} = a_{1} X_{1} + ... + a_{N} X_{N} [/tex]

[tex] Y = a_{1} X_{1} + ... + a_{N} X_{N} [/tex]

then [tex] bX_{1} = Y - a_{2} X_{2} ... - a_{N} X_{N} [/tex]

so i can see that [tex] bX_{1} = span{Y,X_{2},...,X_{N}} [/tex]

also we know that X 1 has a unique representation as a span of the Xi, where i is not 1

but i m not sure how connect the two...

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# Homework Help: More linear algebra

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