Multiply the Matrices

Problem

[[1/4,−9/26,7/52],[1/4,−1/26,−5/52],[1/4,5/26,−1/52]]*[[8],[1],[10]]

Solution

1. Identify the rule for matrix multiplication, where each element of the resulting vector is the dot product of a row from the first matrix and the column vector.

2. Calculate the first element by multiplying the first row by the vector:

1/4*(8)+(−9/26)*(1)+7/52*(10)

2−9/26+70/52

2−18/52+70/52

2+52/52=3

3. Calculate the second element by multiplying the second row by the vector:

1/4*(8)+(−1/26)*(1)+(−5/52)*(10)

2−1/26−50/52

2−2/52−50/52

2−52/52=1

4. Calculate the third element by multiplying the third row by the vector:

1/4*(8)+5/26*(1)+(−1/52)*(10)

2+5/26−10/52

2+10/52−10/52=2

Final Answer

[[1/4,−9/26,7/52],[1/4,−1/26,−5/52],[1/4,5/26,−1/52]]*[[8],[1],[10]]=[[3],[1],[2]]

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