Multiply the Matrices [[1/5,2/5],[4/5,2/5]][[1,4],[-2,2]]

Problem

[[1/5,2/5],[4/5,2/5]]*[[1,4],[−2,2]]

Solution

1. Identify the rule for matrix multiplication, where the element in row i and column j of the resulting matrix is the dot product of the ith row of the first matrix and the jth column of the second matrix.

2. Calculate the element for the first row, first column:

1/5*(1)+2/5*(−2)=1/5−4/5=−3/5

3. Calculate the element for the first row, second column:

1/5*(4)+2/5*(2)=4/5+4/5=8/5

4. Calculate the element for the second row, first column:

4/5*(1)+2/5*(−2)=4/5−4/5=0

5. Calculate the element for the second row, second column:

4/5*(4)+2/5*(2)=16/5+4/5=20/5=4

6. Assemble the resulting matrix using the calculated values.

Final Answer

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

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