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Unformatted text preview: Practice Midterm 1 Math 20F Lin Winter 2010 Place all books, calculators, and papers under your desk. On the cover of your blue book write your name, student ID number, section time, and color of your exam. In a column number one to four. Show all your work, and box your answers. You must give correct reasons for each answer to obtain full credit. Good luck. 1. Consider the system x 1 + x 3 = 3- x 1 + x 2 + x 3 = 0- x 1- 2 x 2- 3 x 3 = 5 (a) 2 pts. Write the above system in the form Ax = b . Determine the matrices, A , b . (b) 10 pts. Find A- 1 . (c) 4 pts. Find a solution to the system of equations. Is the solution unique? (d) 2 pts. Write b as a linear combination of the columns of A . (Your answer should only involve numbers) (e) 4 pts. Do the columns of A span R 3 ? Give reasons. 2. (a) Let T : R 2 R 2 be a linear transformation. Let ~ e 1 = 1 , ~ e 2 = 1 , ~ y 1 = 2 3 , ~ y 2 =- 1 5 . Suppose T ~ e 1 = ~ y 1 ,T ~ e 2 = ~ y 2 ....
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- Spring '10