Determine which property of determinants the equation illustrates. |1 8 -3 3 - 1

Question

Determine which property of determinants the equation illustrates. |1 8 -3 3 - 12 6 7 4 9| = 12 |1 2 -1 3 -3 2 7 1 3|, |5 0 10 25 -30 40 -15 5 20| = 5^3 |1 0 2 5 -6 8 -3 1 4|, |1 -3 2 5 2 -1 -1 0 6 = |1 -3 2 0 17 -11 -1 0 6|, |3 2 4 -2 1 5 5 -7 -20| = |3 2 -6 -2 1 0 5 -7 15|, |2 1 -1 0 4 1 0 1 3 2 3 6 1 -3 6 0 4 0 2 0 -1 8 5 3 -2| = 0, |4 3 1 9 9 9 -1 2 3 -3 3 4 6 9 12 5 2 0 6 6 6 0 3 0 0| = 0,: Use elementary row or column operations, find the determinant. |3 8 -7 0 -5 4 6 1 6|, |4 3 -2 5 4 1 -2 3 4|, |1 -2 7 9 3 -4 5 5 3 6 1 -1 4 5 3 2|, |1 -1 8 4 2 2 6 0 -4 3 2 0 2 6 2 0 2 8 0 0 0 1 1 2 2|

Explanation / Answer

1) a) If one column is divided by k to gve B then

B = k. A. Also, if two columns are divided by k to gve B .Here, a common factor is taken out of two columns.

Thus, B = k. m. A

b) If one column is divided by k to give B then

B = k. A. Here, a common factor is taken out of three columns.

B = k^3 A

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