MidIISamplev3 - TRUE or FALSE Along with your answer...

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Prof. Ming Gu, 861 Evans, tel: 2-3145 Email: [email protected] http://www.math.berkeley.edu/ mgu/MA110F2011 Math110 Sample Midterm II, Fall 2011 This is a closed book exam; but everyone is allowed a standard one-page cheat sheet (on one-side only). You need to justify every one of your answers unless you are asked not to do so. Completely correct answers given without justification will receive little credit. Problems are not necessarily ordered according to difficulties. You need not simplify your answers unless you are specifically asked to do so. Hand in this exam before you leave. Problem Maximum Score Your Score 1 30 2 20 3 20 4 20 Total 90 Write your personal information below and on top of every page in the test. Your Name: Your GSI: Your SID: 1. Label each of the following statements as
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Unformatted text preview: TRUE or FALSE . Along with your answer, provide a counterexample, an informal proof or an explanation. (a) The determinant is a linear function M n × n ( F ) → F . Name and SID: 2 (b) Every n × n matrix may be written as a product of elementary matrices. Name and SID: 3 (c) If Ax = 0 has exactly one solution, then Ax = b has exactly one solution. Name and SID: 4 2. Use row operations to find the inverse of the matrix -2 1 4-3 1 1 1-1 . Name and SID: 5 3. Let A be an m × n matrix of rank m and let B be an n × p matrix with rank n . Determine the rank of the matrix AB . Name and SID: 6 4. If a matrix B is similar to matrix C , show that B 2 is similar to C 2 ....
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