Multiply the Matrices

Problem

[[3,1,−1],[−1,1,3]]*[[−1.1259,2.2518,−1.1259],[2.2512,−4.5036,2.2518],[−1.1259,2.2518,−1.1259]]

Solution

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

2. Calculate the first row, first column entry by taking the dot product of the first row of the first matrix and the first column of the second matrix.

3*(−1.1259)+1*(2.2512)+(−1)*(−1.1259)=−3.3777+2.2512+1.1259=−0.0006

3. Calculate the first row, second column entry.

3*(2.2518)+1*(−4.5036)+(−1)*(2.2518)=6.7554−4.5036−2.2518=0

4. Calculate the first row, third column entry.

3*(−1.1259)+1*(2.2518)+(−1)*(−1.1259)=−3.3777+2.2518+1.1259=0

5. Calculate the second row, first column entry.

−1*(−1.1259)+1*(2.2512)+3*(−1.1259)=1.1259+2.2512−3.3777=−0.0006

6. Calculate the second row, second column entry.

−1*(2.2518)+1*(−4.5036)+3*(2.2518)=−2.2518−4.5036+6.7554=0

7. Calculate the second row, third column entry.

−1*(−1.1259)+1*(2.2518)+3*(−1.1259)=1.1259+2.2518−3.3777=0

8. Assemble the results into the final matrix. Note that the small values near zero (−0.0006 suggest the intended result is likely zero, but we provide the calculated values.

Final Answer

[[3,1,−1],[−1,1,3]]*[[−1.1259,2.2518,−1.1259],[2.2512,−4.5036,2.2518],[−1.1259,2.2518,−1.1259]]=[[−0.0006,0,0],[−0.0006,0,0]]

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