MATH-205 Midterm: Bates MATH 205 032307greer205exam
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Your grade is based on correctness, completeness, and clarity on each exercise. You may use a calculator, but no notes, books, or other students. Use the invertible matrix theorem to answer the following questions. In each of them, assume the matrix a is n n. also, for each of them, fully explain your reasoning. a. ) (5 pts. ) If there is an n n matrix d for which ad = i, is there also an n n matrix. C for which ca = i? b. ) (5 pts. ) If at is not invertible, is a invertible? c. ) (5 pts. ) A = compute a basis for col a and a basis for nul a. In each of the following, assume the matrix a is 3 3. Also, for each of them, fully explain your reasoning. a. ) (5 pts. ) Why is det at a 0? b. ) (5 pts. ) Is det(4a) = 4 det a? c. ) (5 pts. )
