-- Sep 6 In-Class Exercise Thread
A = [1,2,3; 4,5,6; 7,8,9]
Since A is multilinear, the following can be applied:
Det(A) = |1,2,3; 4,5,6; 7, 8, 9|
= |1,2,3; 4,5,6; 7, 8, 9| - 4*|0, 0, 0; 1, 2, 3; 0, 0, 0|
= |1, 2, 3; 0, -3, -6; 7, 8, 9| - 7 |0, 0, 0; 0, 0, 0; 1, 2, 3|
= |1, 2, 3; 0, -3, -6; 0, -6, -12| + 2 |0, 0, 0; 0, 0, 0; 0, -3, -12|
= |1, 2, 3; 0, -3, -6; 0, 0, 0|
= 0
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Edited: 2017-09-06)
A = [1,2,3; 4,5,6; 7,8,9]
Since A is multilinear, the following can be applied:
Det(A) = |1,2,3; 4,5,6; 7, 8, 9|
= |1,2,3; 4,5,6; 7, 8, 9| - 4*|0, 0, 0; 1, 2, 3; 0, 0, 0|
= |1, 2, 3; 0, -3, -6; 7, 8, 9| - 7 |0, 0, 0; 0, 0, 0; 1, 2, 3|
= |1, 2, 3; 0, -3, -6; 0, -6, -12| + 2 |0, 0, 0; 0, 0, 0; 0, -3, -12|
= |1, 2, 3; 0, -3, -6; 0, 0, 0|
= 0