Multiply the Matrices [[2/3,1/4],[1/3,3/4]][[1950],[2850]]

Problem

[[2/3,1/4],[1/3,3/4]]*[[1950],[2850]]

Solution

1. Identify the dimensions of the matrices. The first matrix is 2×2 and the second is 2×1 so the resulting matrix will be 2×1

2. Calculate the first entry of the product by multiplying the first row of the first matrix by the column of the second matrix.

2/3*(1950)+1/4*(2850)

3. Simplify the first entry calculation.

2*(650)+712.5=1300+712.5=2012.5

4. Calculate the second entry of the product by multiplying the second row of the first matrix by the column of the second matrix.

1/3*(1950)+3/4*(2850)

5. Simplify the second entry calculation.

650+3*(712.5)=650+2137.5=2787.5

Final Answer

[[2/3,1/4],[1/3,3/4]]*[[1950],[2850]]=[[2012.5],[2787.5]]

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