Multiply the Matrices [[-3,1],[5,-2]]*[[4,0,-2],[-3,1,1]]

Problem

[[−3,1],[5,−2]]*[[4,0,−2],[−3,1,1]]

Solution

1. Identify the dimensions of the matrices to ensure they can be multiplied. The first matrix is 2×2 and the second is 2×3 so the resulting matrix will be 2×3

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

(c_11)=(−3)*(4)+(1)*(−3)=−12−3=−15

(c_12)=(−3)*(0)+(1)*(1)=0+1=1

(c_13)=(−3)*(−2)+(1)*(1)=6+1=7

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

(c_21)=(5)*(4)+(−2)*(−3)=20+6=26

(c_22)=(5)*(0)+(−2)*(1)=0−2=−2

(c_23)=(5)*(−2)+(−2)*(1)=−10−2=−12

4. Assemble the calculated values into the final 2×3 matrix.

Final Answer

[[−3,1],[5,−2]]*[[4,0,−2],[−3,1,1]]=[[−15,1,7],[26,−2,−12]]

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