document.write( "Question 135207: The vector v=[4 5] can be written as a linear combination of the vectors v1=[1 3] and v2=[4 -2] by letting c1=? and c2=?. Find c1 and c2 to solve. \n" ); document.write( "
Algebra.Com's Answer #99034 by Edwin McCravy(20055)\"\" \"About 
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document.write( "    v = c1v1 + c2v2\r\n" );
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document.write( "[4 5] = c1[1 3] + c2[4 -2]\r\n" );
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document.write( "[4 5] = [c1*1 c1*3] + [c2*4 c2*-2]\r\n" );
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document.write( "[4 5] = [c1 3c1] + [4c2 -2c2]\r\n" );
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document.write( "[4 5] = [c1+4c2  3c1-2c2]\r\n" );
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document.write( "Equating first components give the equation\r\n" );
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document.write( "4 = c1 + 4c2\r\n" );
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document.write( "Equating second components gives the equation\r\n" );
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document.write( "5 = 3c1 - 2c2\r\n" );
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document.write( "So we have this system of equations:\r\n" );
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document.write( "4 =  c1 + 4c2\r\n" );
document.write( "5 = 3c1 - 2c2\r\n" );
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document.write( "Or\r\n" );
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document.write( " c1 + 4c2 = 4 \r\n" );
document.write( "3c1 - 2c2 = 5\r\n" );
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document.write( "Solve that system of equations and get\r\n" );
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document.write( "c1 = 2, c2 = 1/2\r\n" );
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document.write( "Edwin

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