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k is linearly independent v vv 11 prove or disprove

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Unformatted text preview: {￿1 , . . . , ￿k } be a linearly independent set in Rn . Prove that if ￿ ￿∈ span B , v v v then {￿1 , . . . , ￿k , ￿ } is linearly independent. v vv 11. Prove or disprove each of the following statements a) The rank of a matrix is the number of rows in the RREF of the matrix that are composed entirely of zeroes. 1 1 is a solution of a homogeneous system of linear equations, then the system has b) If 1 infinitely many solutions. c) Let ￿ , ￿ ￿ ∈ Rn , ￿ ￿= 0. If ￿ · ￿ = ￿ · ￿, then ￿ = ￿. a b, c a ab ac bc d) Let ￿ , ￿ ∈ R3 such that {￿ , ￿ } is linearly independent. If w is orthogonal to ￿ and ￿ , uv uv ￿ u v then {￿ , ￿ , w} is also linearly independent. uv ￿ e) Let ￿ ￿ ∈ R3 . If ￿ ￿= ￿ then the set with vector equation ￿ = ￿ + t￿ is not a subspace b, v b 0, xb v of R3 . 2...
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This note was uploaded on 01/16/2014 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

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