Multiply the Matrices

Problem

[[68,41,98,51]]*[[44.8,6.2,10.1,7.4,8.1],[52.8,3.8,9.6,6.3,12.4],[47.4,8.3,12.6,8.2,9.7],[50.3,6.2,11.6,9.8,10.7]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 1×4 row vector and the second is a 4×5 matrix. The resulting matrix will be a 1×5 row vector.

2. Calculate the first element by taking the dot product of the row and the first column.

68*(44.8)+41*(52.8)+98*(47.4)+51*(50.3)=3046.4+2164.8+4645.2+2565.3=12421.7

3. Calculate the second element by taking the dot product of the row and the second column.

68*(6.2)+41*(3.8)+98*(8.3)+51*(6.2)=421.6+155.8+813.4+316.2=1707

4. Calculate the third element by taking the dot product of the row and the third column.

68*(10.1)+41*(9.6)+98*(12.6)+51*(11.6)=686.8+393.6+1234.8+591.6=2906.8

5. Calculate the fourth element by taking the dot product of the row and the fourth column.

68*(7.4)+41*(6.3)+98*(8.2)+51*(9.8)=503.2+258.3+803.6+499.8=2064.9

6. Calculate the fifth element by taking the dot product of the row and the fifth column.

68*(8.1)+41*(12.4)+98*(9.7)+51*(10.7)=550.8+508.4+950.6+545.7=2555.5

Final Answer

[[68,41,98,51]]*[[44.8,6.2,10.1,7.4,8.1],[52.8,3.8,9.6,6.3,12.4],[47.4,8.3,12.6,8.2,9.7],[50.3,6.2,11.6,9.8,10.7]]=[[12421.7,1707,2906.8,2064.9,2555.5]]

Want more problems? Check here!