document.write( "Question 1095299: Demonstrate that vectors (1,0,0),(0,1,0),(0,0,1),(0,1,1) are not an efficient spanning set by showing that an arbitrary vector in R3 can be expressed in more than one way as a linear combination of these vectors.\r
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Algebra.Com's Answer #709916 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Let me make writing more understandable for this problem.\r\n" );
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document.write( "Let  i = (1,0,0) be the first given vector,\r\n" );
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document.write( "     j = (0,1,0) be the second given vector,\r\n" );
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document.write( "and  k = (0,0,1) be the third given vector.\r\n" );
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document.write( "We also have m = (0,1,1) as the fourth given vector.\r\n" );
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document.write( "Let  c = a*i + b*j + c*k  be an arbitrary vector of your 3D space.\r\n" );
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document.write( "Then it has TWO different presentations.\r\n" );
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document.write( "One is this  c = a*i + b*j + c*k.                  (1)\r\n" );
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document.write( "The second is this:  c = a*i + b*m + (c-b)*k.      (2)\r\n" );
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document.write( "      (Check it by considering its by-component parts.)\r\n" );
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document.write( "These two presentations of the same vector give you the example you are looking for.\r\n" );
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