Review1-HW5 - Math 225 Review problems for midterm 1 Read...

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Math 225 Review problems for midterm 1 Read your lecture notes and the textbook (Sections 1.1-1.5, 1.7, 2.1, 2.2) be sure you are able to do all the exercices from homework 1-5. Below you can find some extra review problems. The problems from this review sheet are the homework 5 assignment and will be graded (due on Thursday Feb 26) . 1. Let A 1 , A 2 be the following matrices A 1 = 1 1 1 1 2 1 1 1 3 2 2 3 , A 2 = 1 1 1 1 2 1 1 1 3 2 2 2 , Solve the equations A 1 x = b , A 2 x = b indicating the pivot positions and free variables, for (a) b = 1 1 3 ; (b) b = 1 1 0 , (c) b = 0 0 0 . 2. Write down the solutions of the systems in problem 1 in a parametric vector form. 3. Explain the relation between the solution sets of systems of linear equations (SLEs) Ax = b and Ax = 0, and give an example of your choice. 4. Let x 1 = 1 2 3 and x 2 = 1 4 5 be solutions of a SLE Ax = b . Find one more solution of the equation.
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