document.write( "Question 1182572: Define T : R^2 → R^2 by T(a1, a2) = (a1, −a2). Prove that T is linear, and find kernel and range of T.
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Algebra.Com's Answer #812646 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "This map is the reflection of a coordinate plane about x-axis.\r\n" );
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document.write( "The kernel is 0 (zero; zero vector).\r\n" );
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document.write( "The range is the entire R^2, i.e. whole coordinate plane.\r\n" );
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document.write( "The fact that it is linear map is OBVIUOS; but you can check it formally on your own, \r\n" );
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document.write( "if you know the definition of a linear map.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Read your textbook.\r
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\n" ); document.write( "\n" ); document.write( "Or you write your own, instead of reading the existing textbooks ?\r
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\n" ); document.write( "\n" ); document.write( "By the way, what university are you and what is your Algebra textbook ?\r
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