Multiply the Matrices (1/0.18)*[[0.6,-0.6],[-0.5,0.8]]

Problem

1/0.18*[[0.6,−0.6],[−0.5,0.8]]

Solution

1. Simplify the scalar fraction by multiplying the numerator and denominator by 100 to remove decimals.

1/0.18=100/18

2. Reduce the fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor, which is 2.

100/18=50/9

3. Distribute the scalar 50/9 to each element inside the matrix.

[[50/9*(0.6),50/9*(−0.6)],[50/9*(−0.5),50/9*(0.8)]]

4. Calculate the product for each entry, converting the decimals to fractions (0.6=6/10 −0.5=−5/10 0.8=8/10 to simplify the multiplication.

50/9⋅6/10=300/90=10/3

50/9⋅−6/10=−300/90=−10/3

50/9⋅−5/10=−250/90=−25/9

50/9⋅8/10=400/90=40/9

Final Answer

1/0.18*[[0.6,−0.6],[−0.5,0.8]]=[[10/3,−10/3],[−25/9,40/9]]

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