Multiply the Matrices [[2,-1,4]][[1],[3],[5]]

Problem

[[2,−1,4]]*[[1],[3],[5]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 1×3 row vector and the second matrix is a 3×1 column vector. Since the number of columns in the first matrix matches the number of rows in the second, the result will be a 1×1 matrix (a scalar).

2. Apply the dot product formula for matrix multiplication. Multiply each corresponding element from the row of the first matrix and the column of the second matrix, then sum the products.

2*(1)+(−1)*(3)+4*(5)

3. Calculate the individual products.

2−3+20

4. Simplify the expression to find the final sum.

−1+20=19

Final Answer

[[2,−1,4]]*[[1],[3],[5]]=19

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