document.write( "Question 22538: Let L: R^2 -> R^2 be a linear operator. If
\n" ); document.write( "L((1,2)^T)=(-2,3)^T and L((1,-1)^T)=(5,2)^T
\n" ); document.write( "determine the value of L((7,5)^T)
\n" ); document.write( "The answer in the back of the book was (7,18)^T but I dont know the steps of how to get that solution \n" ); document.write( "
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L((1,2)^T)=(-2,3)^T and L((1,-1)^T)=(5,2)^T
\n" ); document.write( "determine the value of L((7,5)^T)
\n" ); document.write( "The answer in the back of the book was (7,18)^T\r
\n" ); document.write( "\n" ); document.write( " Solve : (7,5) = a(1,2) + b(1,-1)
\n" ); document.write( " We have a+b = 7
\n" ); document.write( " and 2a-b = 5.\r
\n" ); document.write( "\n" ); document.write( " Hence, a=4, b =3.
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\n" ); document.write( " So,L((7,5)^T) = L(4(1,2)T + 3(1,-1)^T)
\n" ); document.write( " = 4 L ((1,2)^T) + 3 L ((1,-1)^T)
\n" ); document.write( " = ...\r
\n" ); document.write( "\n" ); document.write( " Note, {{1,2)^T,(1,-1)^T} forms a basis of R^2.\r
\n" ); document.write( "\n" ); document.write( " You have to work hard.\r
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\n" ); document.write( " Kenny\r
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