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Unformatted text preview: A = 4 1 , B = 2 -3-1 5 1 3 . For what values(s) of is A singular? What about for B ? (5) (Determinant of an Upper-Triangular Matrix, P. 157 #6) Let U be an n n upper triangular matrix. Show that det U = u 11 u 22 u 33 u nn . 1 2 (6) (Elementary Matrices) Let B be a 4 4 matrix to which we apply the following operations, in order. Interchange columns 2 and 3, Divide column 1 by 6, Multiply row 4 by 5, Add row 1 to row 3, Replace row 1 by row 4, Subtract column 4 from each of the other columns, Delete row 2 (so the number of rows is now 3). (a) Write the result as a product of eight matrices, including B . (b) Write the result as a product of three matrices, including B ....
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