Multiply the Matrices [[12],[10]]*[[7,14]]

Problem

[[12],[10]]*[[7,14]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 2×1 column vector and the second matrix is a 1×2 row vector.

2. Determine the size of the resulting matrix. Since the inner dimensions match (1 = 1),t*h*e*p*r*o*d(u)*c*t*e*x*i*s(t)*s(a)*n*d(w)*i*l*l*b*e*a \times 2$ matrix.

3. Calculate the element at row 1, column 1 by multiplying the first element of the first matrix by the first element of the second matrix.

12×7=84

4. Calculate the element at row 1, column 2 by multiplying the first element of the first matrix by the second element of the second matrix.

12×14=168

5. Calculate the element at row 2, column 1 by multiplying the second element of the first matrix by the first element of the second matrix.

10×7=70

6. Calculate the element at row 2, column 2 by multiplying the second element of the first matrix by the second element of the second matrix.

10×14=140

7. Assemble the results into the final 2×2 matrix.

Final Answer

[[12],[10]]*[[7,14]]=[[84,168],[70,140]]

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