Determine which property of determinants the equation illustrates. (a) |1 3 7 8

Question

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