Multiply the Matrices

Problem

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

Solution

1. Identify the dimensions of the matrices to ensure multiplication is possible. The first matrix is 4×3 and the second is 3×3 The resulting matrix will be 4×3

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

(1)*(3)+(0)*(0)+(0)*(0)=3

(1)*(1)+(0)*(−1)+(0)*(0)=1

(1)*(−1)+(0)*(−1)+(0)*(−1)=−1

3. Calculate the second row of the product.

(−3)*(3)+(1)*(0)+(0)*(0)=−9

(−3)*(1)+(1)*(−1)+(0)*(0)=−4

(−3)*(−1)+(1)*(−1)+(0)*(−1)=2

4. Calculate the third row of the product.

(2)*(3)+(1)*(0)+(1)*(0)=6

(2)*(1)+(1)*(−1)+(1)*(0)=1

(2)*(−1)+(1)*(−1)+(1)*(−1)=−4

5. Calculate the fourth row of the product.

(0)*(3)+(−2)*(0)+(1)*(0)=0

(0)*(1)+(−2)*(−1)+(1)*(0)=2

(0)*(−1)+(−2)*(−1)+(1)*(−1)=1

6. Assemble the results into the final 4×3 matrix.

Final Answer

[[1,0,0],[−3,1,0],[2,1,1],[0,−2,1]]*[[3,1,−1],[0,−1,−1],[0,0,−1]]=[[3,1,−1],[−9,−4,2],[6,1,−4],[0,2,1]]

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