Use Gauss operations to reduce matrices A and B below to upper triangular form a

Question

Use Gauss operations to reduce matrices A and B below to upper triangular form and evaluate their determinant, where A = |1 2 3 2 4 1 1 4 4|, B =|1 3 5 -1 4 2 3 -2 4|. Use Gauss operations to prove the formula |1 a a2 1 b b2 1 c c2|=(b-a)(c-a)(c-b).

Explanation / Answer

1 2 3 2 4 1 1 4 4 row 3 -> row3 - row1 1 2 3 0 0 -5 0 2 1 1 2 3 0 2 1 0 0 -5 answer B = 1 3 5 -1 4 2 3 -2 4 1 3 5 0 7 7 0 -11 -11 1 3 5 0 7 7 0 0 0 answer 1 a a*a 1 b b*b 1 c c*c row 2 -> row2 - row1 , row3 -> row3 - row1 1 a a*a 0 b-a b*b -a*a 0 c-a c*c -a*a expand along column 1 : (b-a)[c-a][c+a] - [c-a][b-a][b+a] : (b-a)(c-a)[ c+a - b - a ] (b-a)(c-a)(c-b) answer !!!

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