Multiply the Matrices

Problem

[[10,7],[14,3]]*[[−3/34,7/34],[7/34,−5/34]]

Solution

1. Identify the rule for matrix multiplication, where the element in row i and column j of the resulting matrix is the dot product of row i of the first matrix and column j of the second matrix.

2. Calculate the element at row 1, column 1 by multiplying the first row of the first matrix by the first column of the second matrix.

10⋅(−3/34)+7⋅(7/34)=−30/34+49/34=19/34

3. Calculate the element at row 1, column 2 by multiplying the first row of the first matrix by the second column of the second matrix.

10⋅(7/34)+7⋅(−5/34)=70/34−35/34=35/34

4. Calculate the element at row 2, column 1 by multiplying the second row of the first matrix by the first column of the second matrix.

14⋅(−3/34)+3⋅(7/34)=−42/34+21/34=−21/34

5. Calculate the element at row 2, column 2 by multiplying the second row of the first matrix by the second column of the second matrix.

14⋅(7/34)+3⋅(−5/34)=98/34−15/34=83/34

6. Assemble the resulting matrix using the calculated values.

Final Answer

[[10,7],[14,3]]*[[−3/34,7/34],[7/34,−5/34]]=[[19/34,35/34],[−21/34,83/34]]

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