document.write( "Question 1167649: Suppose u, v ∈ R3. Determine if the function
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Algebra.Com's Answer #852203 by ikleyn(52906) $\"\"$ $\"About$

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\n" ); document.write( "Suppose u, v ∈ R3. Determine if the function
\n" ); document.write( "⟨u, v⟩ = 2u1v1 + u2v2 + 4u3v3
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document.write( "In  ,  consider linear transformation\r\n" );
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document.write( "                        A\r\n" );
document.write( "    ( , ,  ) ---->  Au = ( , ,  ).\r\n" );
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document.write( "It is clear that \r\n" );
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document.write( "     +  +  = (Au,Av).\r\n" );
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document.write( "So, the given function is an inner product.\r\n" );
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document.write( "QED.\r\n" );
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