Unformatted text preview: } What is the rank of T ? Explain. 3. [Basis] Let S = { x 1 ,...,x m } be a set of linearly independent vectors in R n , with m < n, and let T = { y 1 ,...,y n } be a set of basis vectors of R n . Show that there are ( nm ) vectors in the set T, such that the m vectors in S, together with these ( nm ) vectors in T, constitute a basis of R n . 4. [Inner Product] Suppose S = { x 1 ,...,x n } is a set of nonnull vectors in R n , which are mutually orthogonal: that is, x i x j = 0 whenever i 6 = j. Show that S is linearly independent. 1...
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 Fall '08
 MITRA
 Linear Algebra, Vectors, linearly independent vectors

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