Multiply the Matrices [[5,6],[6,5]][[24],[23]]

Problem

[[5,6],[6,5]]*[[24],[23]]

Solution

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

2. Calculate the first entry of the product by multiplying the first row of the first matrix by the column of the second matrix.

5⋅24+6⋅23

3. Simplify the arithmetic for the first entry.

120+138=258

4. Calculate the second entry of the product by multiplying the second row of the first matrix by the column of the second matrix.

6⋅24+5⋅23

5. Simplify the arithmetic for the second entry.

144+115=259

Final Answer

[[5,6],[6,5]]*[[24],[23]]=[[258],[259]]

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