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Unformatted text preview: R n n , is the equation ( A + B ) 2 = A 2 +2 AB + B 2 still true? If so, prove it, if not, nd examples of matrices A and B for which this fails. 4. Let A = 2 4 8 4 5 1 7 9 3 . (a) Find ker A and im A as spans of vectors. 3 (b) Find all solutions of the system A x = b , where b = 6 9 16 . 5. Consider the basis = 1 1 , 1 2 for R 2 . Find the representation [ x ] of the vector x = 2 5 in this basis. 6. Let = { e 1 , e 2 } be the standard basis for R 2 and let = 1 1 , 1 be another basis for R 2 . If T A L ( R 2 , R 2 ) is the counterclockwise rotation through / 4, with associated matrix A = " 1 21 2 1 2 1 2 # nd the matrix representation [ T A ] , of T A in these bases. 4...
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 Spring '12
 DavidGlenn
 Linear Algebra, Algebra, Equations

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