Multiply the Matrices

Problem

[[12/8,−1/2,−1/8],[−15/8,1/2,3/8],[5/4,0,−1/4]]*[[1],[−1],[1]]

Solution

1. Simplify the fractions in the first matrix to make calculations easier.

[[3/2,−1/2,−1/8],[−15/8,1/2,3/8],[5/4,0,−1/4]]*[[1],[−1],[1]]

2. Set up the matrix multiplication by multiplying each row of the first matrix by the column vector.

[[(3/2)*(1)+(−1/2)*(−1)+(−1/8)*(1)],[(−15/8)*(1)+(1/2)*(−1)+(3/8)*(1)],[(5/4)*(1)+(0)*(−1)+(−1/4)*(1)]]

3. Calculate the product for the first row using a common denominator of 8.

3/2+1/2−1/8=12/8+4/8−1/8=15/8

4. Calculate the product for the second row using a common denominator of 8.

−15/8−1/2+3/8=−15/8−4/8+3/8=−16/8=−2

5. Calculate the product for the third row.

5/4+0−1/4=4/4=1

Final Answer

[[12/8,−1/2,−1/8],[−15/8,1/2,3/8],[5/4,0,−1/4]]*[[1],[−1],[1]]=[[15/8],[−2],[1]]

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