Algebra.Com's Answer #783057 by ikleyn(52803)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Linear operator L acts on vectors  , by mapping each such vector into the vector \r\n" );
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document.write( " L : ---->  .\r\n" );
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document.write( "Therefore, the kernel of the operator L are those vectors , for which 2x1 + x2 = 0.\r\n" );
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document.write( "They are all the vectors of the form  .\r\n" );
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document.write( "They form 1D-space (= actually, a line) spanned on the vector (-1,2) on the standard coordinate plane.\r\n" );
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document.write( "It is the same as to say that the kernel is the line 2y = -x on standard (x,y) coordinate plane, or, equivalently,\r\n" );
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document.write( "the line x + 2y = 0.\r\n" );
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document.write( "The image of this operator L is the 1D-space {(x,0)} - same as the x-axis on the standard coordinate plane (x,y).\r\n" );
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document.write( "Answered, explained, solved and completed.\r
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document.write( "Hey, if you really are a student, learning Linear Algebra, can you post me the names of the books/textbooks, \r
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document.write( "recommended to you by your teacher/professor/lecturer ?\r
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document.write( "May be, I will be able to add my recommendations to your list.\r
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