midterm2B - Linear Algebra - Midterm IIB Your Name: Do not...

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Linear Algebra - Midterm IIB Your Name: Do not open this until you are told to do so. Please turn of your cell phone. Show all your work on this booklet. The blue books are For scratch work only. Calculators, books, class notes and Formula sheets are NOT allowed in this exam. All your answers must be accompanied by calcutations or/and explanations. 7 problems Good luck! Problem 1 /7 = 2 + 3 + 2 Problem 2 /10 = 4 + 3 + 3 Problem 3 /11 = 3 + 5 + 3 Problem 4 /14 = 3 + 2 + 3 + 4 + 2 Problem 5 /6 Problem 6 /5 Problem 7 /6 Total points /59
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1 Problem 1 Consider the linear trasformation T( x y z ) = - x + 2 y + z 2 x - z - x + y + z a) Find the standard matrix A associated to T (not by reading coe±cients). b) Compute the determinant of A. c) Determine if T is invertible or not.
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2 Problem 2 Let B = { 1 0 0 , 1 1 0 , 2 1 1 } . a) Prove that B is a basis for R 3 . b) Find the coordinate vector of v = - 4 3 1 with respect to B .
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This homework help was uploaded on 04/11/2008 for the course MATH 2010 taught by Professor Ciperani during the Spring '08 term at Columbia.

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midterm2B - Linear Algebra - Midterm IIB Your Name: Do not...

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