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**Unformatted text preview: **A = ± α 4 1 α ² , B = 2 α-3-1 5 1 3 α . For what values(s) of α 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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- Winter '08
- LinZhi
- Math, Determinant, Numerical Analysis, Matrix Operations, Characteristic polynomial, Triangular matrix, Laguerre