Multiply the Matrices [[2,3]]*[[3,4]]

Problem

[[2,3]]*[[3],[4]]

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), the product is defined and will result in a 1×1 matrix.

3. Apply the dot product formula for matrix multiplication by multiplying corresponding elements and summing them.

2⋅3+3⋅4

4. Calculate the products of the individual terms.

6+12

5. Simplify the expression to find the final value.

18

Final Answer

[[2,3]]*[[3],[4]]=[(18)]

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