Multiply the Matrices [[2,-2],[-11,1]][[0,-2],[5,1]]

Problem

[[2,−2],[−11,1]]*[[0,−2],[5,1]]

Solution

1. Identify the dimensions of the matrices. Both are 2×2 matrices, so the resulting matrix will also be 2×2

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

2*(0)+(−2)*(5)=0−10=−10

3. Calculate the element in the first row, second column by taking the dot product of the first row of the first matrix and the second column of the second matrix.

2*(−2)+(−2)*(1)=−4−2=−6

4. Calculate the element in the second row, first column by taking the dot product of the second row of the first matrix and the first column of the second matrix.

−11*(0)+1*(5)=0+5=5

5. Calculate the element in the second row, second column by taking the dot product of the second row of the first matrix and the second column of the second matrix.

−11*(−2)+1*(1)=22+1=23

6. Assemble the resulting matrix using the calculated values.

Final Answer

[[2,−2],[−11,1]]*[[0,−2],[5,1]]=[[−10,−6],[5,23]]

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