Multiply the Matrices

Problem

[[−1/2,3/10,3/5],[0,−2/5,1/5],[1/2,−1/10,−1/5]]*[[32],[−40],[55]]

Solution

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

2. Calculate the first element of the resulting vector by summing the products of the first row and the column.

(−1/2)*(32)+(3/10)*(−40)+(3/5)*(55)

−16−12+33=5

3. Calculate the second element of the resulting vector by summing the products of the second row and the column.

(0)*(32)+(−2/5)*(−40)+(1/5)*(55)

0+16+11=27

4. Calculate the third element of the resulting vector by summing the products of the third row and the column.

(1/2)*(32)+(−1/10)*(−40)+(−1/5)*(55)

16+4−11=9

5. Combine the results into a single column vector.

Final Answer

[[−1/2,3/10,3/5],[0,−2/5,1/5],[1/2,−1/10,−1/5]]*[[32],[−40],[55]]=[[5],[27],[9]]

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