Let S = {UI. U2 ..... UI'} be a set of vectors in a vector space and let T = (VI. ~ ..

Chapter 4, Problem 26

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Let S = {UI. U2 ..... UI'} be a set of vectors in a vector space and let T = (VI. ~ .. . .. vN,I. where each Vj. i = I. 2 . .. .. //I. is a linear combination of the vectors in 5. Prove that w= bl v l+b2V2+' ,+b .. vm IS a linear combination of the I'ectors in S.

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