Simplify the Matrix

Problem

[[1,1,1/(a2+b2−2*a*b)],[0,0,−1/(a−b)],[0,0,1]]

Solution

1. Identify the algebraic identity in the denominator of the first row, third column.

2. Factor the expression a2+b2−2*a*b using the perfect square trinomial formula.

a2−2*a*b+b2=(a−b)2

3. Substitute the factored form back into the matrix.

[[1,1,1/((a−b)2)],[0,0,−1/(a−b)],[0,0,1]]

Final Answer

[[1,1,1/(a2+b2−2*a*b)],[0,0,−1/(a−b)],[0,0,1]]=[[1,1,1/((a−b)2)],[0,0,−1/(a−b)],[0,0,1]]

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