Practice Problems Math 235 Fall 2010 for Midterm on October 51. a: Solve the system of equations using row operations.x+y-z=62x-y=03x-y-2z=-3b: Write the above system of equations as a matrix equation.c: For what vectorsv=0@abc1Adoes the equationAx=vhave a solution ifA=0@1010-121-131A,andx=0@x1x2x31A.d: What is the rank of the matrixA.e: How many free variables does the matrixAhave?f: Find a ±nite set of vectors that spans the image ofA.2. a: De±ne what it means for a functionF:Rm!Rnto be a linear transformation.b: Are the following linear transformations? Why? Note that the why part of thequestion is very important.
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This note was uploaded on 11/22/2011 for the course MATH 235 taught by Professor Markman during the Fall '08 term at UMass (Amherst).