Math254Mid3

Math254Mid3 - Math 254 Name: _ MIDTERM 3 MATH 254 - SUMMER...

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Math 254 Name: ________________________ MIDTERM 3 MATH 254 - SUMMER 2002 - KUNIYUKI CHAPTERS 6, 7 GRADED OUT OF 75 POINTS ¥ 2 = 150 POINTS TOTAL Circle your final answers! Show all work and simplify wherever appropriate, as we have done in class! A scientific calculator is allowed on this exam. 1) The linear transformation TR R : 23 Æ is such that T 11 3 41 ,, , ()( ) =- and T 01 153 , () ( ) = . Find T 45 , . Hint: Remember the definition of a linear transformation. (5 points) 2) The linear transformation R : 22 Æ is such that Tvv v v v v 12 1 2 1 2 3 ( ) + . Find the preimage of 17 5 , . (7 points)
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3) The linear transformation TR R : 57 Æ is such that dim Ker T () = 3 . (11 points total) a) What is the domain of T ? b) What is nullity T ? c) What is rank T ? d) True or False: Range T is a subspace of R 7 . Circle one: True False e) True or False: Ker T is a subspace of R 7 . Circle one: True False 4) R : 22 Æ is a linear transformation such that, relative to the standard basis of R 2 , Txy T x yx y ,, ( ) =- + 34 . Another basis for R 2 is given by: ¢ = ( ) {} B 13 20 ,,, . (13 points total) a) Find the standard matrix for T . (3 points) b) Find the matrix for T
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This note was uploaded on 09/08/2011 for the course MATH 254 taught by Professor Howard during the Spring '09 term at Mesa CC.

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Math254Mid3 - Math 254 Name: _ MIDTERM 3 MATH 254 - SUMMER...

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