document.write( "Question 1135053: Prove or show a counterexample.
\n" ); document.write( "If v1, v2, v3 are vectors in R4 and v3 is not a linear combination of v1 and v2, then {v1, v2, v3} is a linearly independent set. \n" ); document.write( "

Algebra.Com's Answer #752646 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "The statement is FALSE.\r
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\n" ); document.write( "\n" ); document.write( "The counterexample is below:\r
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document.write( "For example, let  v1  be the zero vector;   let  v2  be the zero vector, too,  and let only v3 is nonzero.\r\n" );
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document.write( "Then  v3  is not a linear combination of v1 and v2,  so the \"if\" condition is satisfied;  but {v1, v2, v3}  IS NOT linearly independent set.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Do not forget to post your \"THANKS\" to me for my work that I have done for you . . . \r
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