Multiply the Matrices

Problem

[[3,−2],[1,0],[−1,4]]*[[5,−1,0],[1,2,−1]]

Solution

1. Check dimensions to ensure the multiplication is defined. The first matrix is 3×2 and the second is 2×3 Since the number of columns in the first equals the number of rows in the second, the resulting matrix will be 3×3

2. Calculate the first row of the product by taking the dot product of the first row of the left matrix with each column of the right matrix.

(c_11)=(3)*(5)+(−2)*(1)=13

(c_12)=(3)*(−1)+(−2)*(2)=−7

(c_13)=(3)*(0)+(−2)*(−1)=2

3. Calculate the second row of the product by taking the dot product of the second row of the left matrix with each column of the right matrix.

(c_21)=(1)*(5)+(0)*(1)=5

(c_22)=(1)*(−1)+(0)*(2)=−1

(c_23)=(1)*(0)+(0)*(−1)=0

4. Calculate the third row of the product by taking the dot product of the third row of the left matrix with each column of the right matrix.

(c_31)=(−1)*(5)+(4)*(1)=−1

(c_32)=(−1)*(−1)+(4)*(2)=9

(c_33)=(−1)*(0)+(4)*(−1)=−4

5. Assemble the results into the final 3×3 matrix.

Final Answer

[[3,−2],[1,0],[−1,4]]*[[5,−1,0],[1,2,−1]]=[[13,−7,2],[5,−1,0],[−1,9,−4]]

Want more problems? Check here!