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Unformatted text preview: Practice Midterm Problems Math 235 Spring 2010 1. a: Write the system of equations below as a matrix equation. b: Find all solutions using Gauss elimination: x 2 y 4 z = 0 , x + 3 y + z = 5 , 2 x + y + 5 z = 3 . 2. What does it mean for a vector to be in the image of a matrix A . Let A be the matrix 1 2 5 2 2 3 1 1 . Is 1 2 1 an element of the image of A ? Why? 3. Define what it means for a set s to be a basis of a subspace V R n . Let A = 1 2 3 1 1 0 1 1 1 4 3 5 . Give a set of vectors that span im( A ) and that are independent. 4. Let A be a n by m matrix, so A gives a linear transformation from R m to R n . Let x 1 ,x 2 R m . Assume that A ( x 1 ) = 0 and that A ( x 2 ) = b .Explain why A ( x 1 + x 2 ) = b 5. Let A be a two by two matrix that rotates by angle 2 / 6. a: Find A . b: Give a geometric explanation why A 6 = I 2 . Here I 2 denotes the 2 by 2 identity matrix....
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This note was uploaded on 11/22/2011 for the course MATH 255 taught by Professor Staff during the Spring '10 term at UMass (Amherst).
 Spring '10
 STAFF
 Linear Algebra, Algebra, Equations

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