MATH 21A Midterm: MATH 20 Harvard 2003Fall20MidtermI
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Full credit may not be given for an answer alone. You may use the backs of the pages or the extra pages for scratch work. Students who, for whatever reason, submit work not their own will ordi- narily be required to withdraw from the college. 1 det b e c a d f g h k. Find the following, with justi cation. (i) (ii) b det c a. The determinant is multilinear in each of its rows, so the answer is. 3 det b e c a d f g h k. In this case the effect is that of multiplying each row by 3, so the deter- minant gets multiplied by 3 three times. Thus the determinant of the given matrix is 33 7 = 27 7 = 189. 1 det e d f g h k c a b. Each trnasposition of the rows introduces a factor of 1.
