Exam I - Fall 2009 - solutions - 11/8/11 5) Verify that ....

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D. Burns Math 272 - Exam I 11/8/11 Answer all questions completely. All questions have equal weight. Use your own paper or the scratch paper provided. Show all necessary work. 1) Determine if the following system is consistent or inconsistent. Explain why. You do not solve the system. The matrix reduces to Since there is a pivot in the 4 th column, the system is inconsistent. 2) Reduce the following matrix to Echelon form. One possible answer…. 3) Write the following system as an augmented matrix , a vector equation and a matrix equation . Do not solve. , , , 4) Let u = and v = . Evaluate the linear combination -2 u + 5 v .
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D. Burns Math 272 - Exam I
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Unformatted text preview: 11/8/11 5) Verify that . Show your work. 6) Find constants c 1 , c 2 , and c 3 so that . By observing problem #5, we see that is a solution. 7) Let and . Solve the matrix equation A x = b completely. reduces to . So . 8) The equation of a plane in can be given in general form by the equation . Find the equation of the plane containing the points (1, -1, 0), (-1, 0, 1) and (0, 1, 1). The three points substituted into the equation leads to the system . The solution is , so the equation of the plane is . The system using the points (1, -1, 0), (-1, 0, 1) and (0, 1, -1) is inconsistent....
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Exam I - Fall 2009 - solutions - 11/8/11 5) Verify that ....

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