Multiply the Matrices

Problem

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

Solution

1. Identify the dimensions of the matrices. Both are 3×3 matrices, so the resulting product will also be a 3×3 matrix.

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

(c_11)=(−1)*(0)+(1)*(1)+(0)*(0)=1

(c_12)=(−1)*(1)+(1)*(1)+(0)*(0)=0

(c_13)=(−1)*(0)+(1)*(0)+(0)*(−1/2)=0

3. Calculate the elements of the second row of the product by multiplying the second row of the left matrix by each column of the right matrix.

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

(c_22)=(1)*(1)+(0)*(1)+(0)*(0)=1

(c_23)=(1)*(0)+(0)*(0)+(0)*(−1/2)=0

4. Calculate the elements of the third row of the product by multiplying the third row of the left matrix by each column of the right matrix.

(c_31)=(0)*(0)+(0)*(1)+(−2)*(0)=0

(c_32)=(0)*(1)+(0)*(1)+(−2)*(0)=0

(c_33)=(0)*(0)+(0)*(0)+(−2)*(−1/2)=1

5. Assemble the resulting matrix using the calculated values.

Final Answer

[[−1,1,0],[1,0,0],[0,0,−2]]*[[0,1,0],[1,1,0],[0,0,−1/2]]=[[1,0,0],[0,1,0],[0,0,1]]

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