2. [ 6.1] Consider the 7 7 matrices 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 3 0 0 2 0 0

Question

2. [ 6.1] Consider the 7 7 matrices 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 3 0 0 2 0 0 0 3 0 0 6 0 0 0 0 0 5 0 0 A=10 0 0 4 0 0 01, B-10 0 0 4 0 0 0 0 0 3 0 0 2 0 0 2 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 3 0 0 6 0 0 0 0 0 0 0 7 We are slightly behind schedule, so our only tool for determinant computation is the "pattern method." For each matrix identify all pattern with non-zero products; determine the number of inversions; the signs of each patteren; and combine to the determinant: (a) Matrix A i. (10pts.) Patterns: ii. (10 pts.) Number of inversions (for each pattern): iii. (10pts.) Sign for each pattern iv. (20 pts.) det(A) -

Explanation / Answer

For A: No of Patterns are 2 (Non Zero entries in each row and column)

No of inversions for each pattern are 6 each

Sign for both the patterns is +ve

Det (A) = 5040 + 1680 = 6720

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