Simplify the Matrix

Problem

[[31/6,−73/18,−16/9],[−73/18,91/18,16/9],[−16/9,16/9,2]]

Solution

1. Identify the common denominator for all entries in the matrix to facilitate factoring.

2. Convert all fractions and integers to have a denominator of 18

31/6=93/18

−16/9=−32/18

16/9=32/18

2=36/18

3. Rewrite the matrix using the common denominator.

[[93/18,−73/18,−32/18],[−73/18,91/18,32/18],[−32/18,32/18,36/18]]

4. Factor out the scalar 1/18 from the matrix to simplify the internal entries to integers.

1/18*[[93,−73,−32],[−73,91,32],[−32,32,36]]

Final Answer

[[31/6,−73/18,−16/9],[−73/18,91/18,16/9],[−16/9,16/9,2]]=1/18*[[93,−73,−32],[−73,91,32],[−32,32,36]]

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