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Unformatted text preview: MATH111 HW 3 Due Date: 2nd, Oct, 2007 (Tue) Please hand in your homework by putting it in the collection box outside MATH dept (Rm 3461, Lift 25-26) Ch1.9 # 14 Let T : R 2 → R 2 be the linear transformation with standard matrix A = [ a 1 a 2 ], where a 1 and a 2 are shown in the figure. Using the figure, draw the image of- 1 3 under the transformation T . Ch1.9 # 16 Fill in the missing entries of the following matrix assuming that the equa- tion holds for all values of the variables. ? ? ? ? ? ? x 1 x 2 = x 1- x 2- 2 x 1 + x 2 x 1 Ch1.9 # 22 Let T : R 2 → R 3 be a linear transformation such that T ( x 1 ,x 2 ) = ( x 1- 2 x 2 ,- x 1 + 3 x 2 , 3 x 1- 2 x 2 ). Find x such that T ( x ) = (- 1 , 4 , 9). Ch1.9 # 32 Let T : R n → R m be a linear transformation, with A its standard matrix. Complete the following statement to make it true: “ T map R n to R m if and only if A has pivot columns.” Find some theorems that explain why the statement is true....
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