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

Problem

[[2,−3],[1,4]]*[[0,−4],[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)+(−3)*(5)=0−15=−15

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*(−4)+(−3)*(1)=−8−3=−11

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:

1*(0)+4*(5)=0+20=20

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:

1*(−4)+4*(1)=−4+4=0

6. Assemble the resulting values into the final matrix structure.

Final Answer

[[2,−3],[1,4]]*[[0,−4],[5,1]]=[[−15,−11],[20,0]]

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