document.write( "Question 1129644: Prove that if {v1, v2, v3} is a linearly independent set of vectors, then so are {v1, v2}, {v1, v3}, {v2, v3}, {v1}, {v2}, and {v3}.\r
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Algebra.Com's Answer #746221 by rothauserc(4718)\"\" \"About 
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A set of vectors is linearly independent if no vector in the set is (a) a scalar multiple of another vector in the set or (b) a linear combination of other vectors in the set
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\n" ); document.write( "for example, the following row vectors are linearly independent
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\n" ); document.write( "v1 = (2, 4, 6)
\n" ); document.write( "v2 = (0, 1, 0)
\n" ); document.write( "v3 = (0, 0, 1)
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\n" ); document.write( "that should get you going
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\n" ); document.write( "Note that if we have
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\n" ); document.write( "v1 = (1, 2, 3)
\n" ); document.write( "v2 = (4, 5, 6)
\n" ); document.write( "v3 = (5, 7, 9)
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\n" ); document.write( "then (v1, v2, v3) is linearly dependent since v3 is a linear combination of v1 and v2
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