Multiply the Matrices [[-3,8]][[4,6]]

Problem

[[−3,8]]*[[4],[6]]

Solution

1. Identify the dimensions of the matrices to ensure multiplication is possible. 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 we are multiplying a 1×2 by a 2×1 the result will be a 1×1 matrix (a single scalar value).

3. Apply the dot product rule for matrix multiplication by multiplying corresponding entries and summing them.

4. Calculate the product of the first elements: −3⋅4=−12

5. Calculate the product of the second elements: 8⋅6=48

6. Sum the results to find the final value: −12+48=36

Final Answer

[[−3,8]]*[[4],[6]]=[(36)]

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