Multiply the Matrices [[7,3]][[1,6,-5],[7,-7,21]]

Problem

[[7,3]]*[[1,6,−5],[7,−7,21]]

Solution

1. Identify the dimensions of the matrices to ensure they can be multiplied. The first matrix is 1×2 and the second matrix is 2×3 Since the number of columns in the first equals the number of rows in the second, the resulting matrix will be 1×3

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

7*(1)+3*(7)=7+21=28

3. Calculate the second element of the product by multiplying the row of the first matrix by the second column of the second matrix.

7*(6)+3*(−7)=42−21=21

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

7*(−5)+3*(21)=−35+63=28

5. Combine the results into a single row matrix.

[[28,21,28]]

Final Answer

[[7,3]]*[[1,6,−5],[7,−7,21]]=[[28,21,28]]

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