Multiply the Matrices [[7,4,7,-4]][[-1],[3],[2],[1]]

Problem

[[7,4,7,−4]]*[[−1],[3],[2],[1]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 1×4 row vector and the second is a 4×1 column vector. The resulting matrix will be a 1×1 scalar.

2. Apply the formula for matrix multiplication by calculating the dot product of the row and the column.

7*(−1)+4*(3)+7*(2)+(−4)*(1)

3. Multiply the individual corresponding elements.

−7+12+14−4

4. Simplify the expression by adding and subtracting the results.

5+14−4

19−4

15

Final Answer

[[7,4,7,−4]]*[[−1],[3],[2],[1]]=15

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