m235_f11prac-page1

m235_f11prac-page1 - Practice Problems Math 235 Fall 2010...

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Practice Problems Math 235 Fall 2010 for Midterm on October 5 1. a: Solve the system of equations using row operations. x + y - z =6 2 x - y =0 3 x - y - 2 z = - 3 b: Write the above system of equations as a matrix equation. c: For what vectors v = 0 @ a b c 1 A does the equation Ax = v have a solution if A = 0 @ 101 0 - 12 1 - 13 1 A ,and x = 0 @ x 1 x 2 x 3 1 A . d: What is the rank of the matrix A. e: How many free variables does the matrix A have? f: Find a ±nite set of vectors that spans the image of A. 2. a: De±ne what it means for a function F : R m ! R n to be a linear transformation. b: Are the following linear transformations? Why? Note that the why part of the question is very important.
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