Sp07_midterm1

Sp07_midterm1 - Name Discussion Section No PID Time Midterm...

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Name: PID: Discussion Section - No: Time: Midterm 1, Math 20F - Lecture B (Spring 2007) Duration: 50 minutes This is a closed-book exam. Calculators are not allowed. You can use one page of notes. To get full credit you should support your answers. There are four questions in this exam. All of the questions have two parts. 1. Consider the system of linear equations 2 x 1 + 4 x 2 - x 3 = 2 x 1 + 2 x 2 + hx 3 = b where h and b are scalars. a) (2.5 points) Explain why the system cannot have a unique solution. b) (2.5 points) For what values of h and b the system is inconsistent. # Score 1 2 3 4 Total

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2. The solution set of the homogeneous system Ax = 0 where A is a 3 by 3 matrix (corre- sponding to a system of three equations in three unknowns) is given by span - 1 1 0 , - 1 0 1 . Let p = 2 3 - 1 be a particular solution satisfying Ax = b for some given vector b of size 3. a) (2 points) Give a solution of the system Ax = b not equal to the particular solution p .
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