Multiply the Matrices [[4,3]]*[[3,3]]

Problem

[[4,3]]*[[3],[3]]

Solution

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

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

3. Apply the dot product rule for matrix multiplication. Multiply the corresponding elements of the row and column and sum them.

4⋅3+3⋅3

4. Calculate the products and the final sum.

12+9=21

Final Answer

[[4,3]]*[[3],[3]]=[21]

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