Multiply the Matrices

Problem

[[7/24,1/12,1/12,1/24],[1/12,7/24,1/24,1/12],[1/12,1/24,7/24,1/12],[1/24,1/12,1/12,7/24]]*[[45],[40],[55],[50]]

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:

7/24*(45)+1/12*(40)+1/12*(55)+1/24*(50)

315/24+80/24+110/24+50/24=555/24=185/8=23.125

3. Calculate the second element of the resulting vector:

1/12*(45)+7/24*(40)+1/24*(55)+1/12*(50)

90/24+280/24+55/24+100/24=525/24=175/8=21.875

4. Calculate the third element of the resulting vector:

1/12*(45)+1/24*(40)+7/24*(55)+1/12*(50)

90/24+40/24+385/24+100/24=615/24=205/8=25.625

5. Calculate the fourth element of the resulting vector:

1/24*(45)+1/12*(40)+1/12*(55)+7/24*(50)

45/24+80/24+110/24+350/24=585/24=195/8=24.375

Final Answer

[[7/24,1/12,1/12,1/24],[1/12,7/24,1/24,1/12],[1/12,1/24,7/24,1/12],[1/24,1/12,1/12,7/24]]*[[45],[40],[55],[50]]=[[23.125],[21.875],[25.625],[24.375]]

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