HW 4 - MATH 225 HOMEWORK 4 pp. 222 223 #2, 4, 8 10, 14 20,...

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MATH 225 HOMEWORK 4 pp. 222 – 223 #2, 4, 8 – 10, 14 – 20, 28 – 30 (only find A 1 , if it exists) pp. 229 – 230 #1 – 3, 5 – 7, 14, 15, 19 p. 232 #22, 24a A. Compute the determinants: i) 1 " 1 1 " 1 1 2 4 8 1 1 1 1 1 " 2 4 " 8 # $ % % % ' ( ( ( ; ii) 1 2 1 0 " 1 3 0 1 " 2 " 4 3 " 8 1 2 11 " 17 # $ % % % ' ( ( ( iii) 1 0 1 0 1 0 1 1 2 3 1 1 0 4 5 0 0 0 6 7 0 0 0 8 9 " # $ $ $ $ % ' ' ' ' ; iv) 1 2 3 4 5 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3 4 " # $ $ $ $ % ' ' ' ' (Subtract row 4 from row 5 , then row 3 from row 4 , etc., leaving the first row unchanged. Then subtract row 3 from row 2 , then row 4 from row 3 , and row 5 from row 4 .) B. Show that the determinant of an upper, or a lower, triangular matrix is the product of the diagonal entries. C. If A M n ( F ) is invertible, show that det(Adj( A )) = (det( A )) n -1 . D. For A M n ( F ) show that A is invertible exactly when Adj( A ) is invertible. E. i) Let
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HW 4 - MATH 225 HOMEWORK 4 pp. 222 223 #2, 4, 8 10, 14 20,...

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