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midterm2B

# 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 off 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 coefficients). b) Compute the determinant of A. c) Determine if T is invertible or not.
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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midterm2B - Linear Algebra Midterm IIB Your Name Do not...

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