Multiply the Matrices [[1,1],[1,2],[1,-1]][[27/7],[-9/7]]

Problem

[[1,1],[1,2],[1,−1]]*[[27/7],[−9/7]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 3×2 matrix and the second is a 2×1 matrix. The resulting matrix will be a 3×1 matrix.

2. Calculate the first row entry by multiplying the first row of the left matrix by the column of the right matrix.

1⋅27/7+1⋅(−9/7)=27/7−9/7=18/7

3. Calculate the second row entry by multiplying the second row of the left matrix by the column of the right matrix.

1⋅27/7+2⋅(−9/7)=27/7−18/7=9/7

4. Calculate the third row entry by multiplying the third row of the left matrix by the column of the right matrix.

1⋅27/7+(−1)⋅(−9/7)=27/7+9/7=36/7

5. Assemble the resulting values into a single column matrix.

Final Answer

[[1,1],[1,2],[1,−1]]*[[27/7],[−9/7]]=[[18/7],[9/7],[36/7]]

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