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1. For each of the following statements determine if it is true or false. If it is true, prove it. If it is false, give an example showing that the statement is false. a) If A, B, C, D are square matrices of the same size then Α Β΄ det = det (AD) - det (BC). b) Let a, b, c, d, e, f, g, h, i € {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If each of the 3-digit numbers abc, def, and ghi is divisible by 10 then a b det d e 9 h i C f = 0. c) Let a, b, c, d, e, f, g, h, i € {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If each of the 3-digit numbers abc, def, and ghi is divisible by 7 then the determinant below is divisible by 7. a b det d e f 9 h i

1. For each of the following statements determine if it is true or false. If it is true, prove it. If it is false, give an example showing that the statement is false. a) If A, B, C, D are square matrices of the same size then Α Β΄ det = det (AD) - det (BC). b) Let a, b, c, d, e, f, g, h, i € {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If each of the 3-digit numbers abc, def, and ghi is divisible by 10 then a b det d e 9 h i C f = 0. c) Let a, b, c, d, e, f, g, h, i € {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If each of the 3-digit numbers abc, def, and ghi is divisible by 7 then the determinant below is divisible by 7. a b det d e f 9 h i

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.5: Determinants
Problem 85E
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4. For each of the following statements determine if it is true or false. If it is true, prove it. If it is false, give an example showing that the statement is false. a) If A, B, C, D are square matrices of the same size then Β] det [B] CD = det (AD) - det (BC). b) Let a, b, c, d, e, f, g, h, i = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If each of the 3-digit numbers abc, def, and ghi is divisible by 10 then a b det d с e f h i a b det d 9 c) Let a, b, c, d, e, f, g, h, i = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If each of the 3-digit numbers abc, def, and ghi is divisible by 7 then the determinant below is divisible by 7. f - e h 2 = 0.
Transcribed Image Text:4. For each of the following statements determine if it is true or false. If it is true, prove it. If it is false, give an example showing that the statement is false. a) If A, B, C, D are square matrices of the same size then Β] det [B] CD = det (AD) - det (BC). b) Let a, b, c, d, e, f, g, h, i = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If each of the 3-digit numbers abc, def, and ghi is divisible by 10 then a b det d с e f h i a b det d 9 c) Let a, b, c, d, e, f, g, h, i = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If each of the 3-digit numbers abc, def, and ghi is divisible by 7 then the determinant below is divisible by 7. f - e h 2 = 0.
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