Multiply the Matrices [[9,10],[10,9]][[20],[24]]

Problem

[[9,10],[10,9]]*[[20],[24]]

Solution

1. Identify the dimensions of the matrices. The first matrix is 2×2 and the second is 2×1 The resulting matrix will be 2×1

2. Calculate the first entry of the product by taking the dot product of the first row of the left matrix and the column of the right matrix.

9*(20)+10*(24)

3. Calculate the second entry of the product by taking the dot product of the second row of the left matrix and the column of the right matrix.

10*(20)+9*(24)

4. Simplify the arithmetic for the first entry.

180+240=420

5. Simplify the arithmetic for the second entry.

200+216=416

Final Answer

[[9,10],[10,9]]*[[20],[24]]=[[420],[416]]

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