Multiply the Matrices

Problem

[[10,5],[−3,8],[2,3],[1,5]]*[[−3,2,10,−9],[3,5,−8,−6]]

Solution

1. Identify the dimensions of the matrices. The first matrix is 4×2 and the second matrix is 2×4 The resulting matrix will be 4×4

2. Calculate the first row of the product by multiplying the first row of the left matrix by each column of the right matrix.

10*(−3)+5*(3)=−30+15=−15

10*(2)+5*(5)=20+25=45

10*(10)+5*(−8)=100−40=60

10*(−9)+5*(−6)=−90−30=−120

3. Calculate the second row of the product.

−3*(−3)+8*(3)=9+24=33

−3*(2)+8*(5)=−6+40=34

−3*(10)+8*(−8)=−30−64=−94

−3*(−9)+8*(−6)=27−48=−21

4. Calculate the third row of the product.

2*(−3)+3*(3)=−6+9=3

2*(2)+3*(5)=4+15=19

2*(10)+3*(−8)=20−24=−4

2*(−9)+3*(−6)=−18−18=−36

5. Calculate the fourth row of the product.

1*(−3)+5*(3)=−3+15=12

1*(2)+5*(5)=2+25=27

1*(10)+5*(−8)=10−40=−30

1*(−9)+5*(−6)=−9−30=−39

Final Answer

[[10,5],[−3,8],[2,3],[1,5]]*[[−3,2,10,−9],[3,5,−8,−6]]=[[−15,45,60,−120],[33,34,−94,−21],[3,19,−4,−36],[12,27,−30,−39]]

Want more problems? Check here!