Multiply the Matrices

Problem

[[1,1,0,0],[0,1,1,0],[0,0,1,1],[0,0,0,1]]*[[1],[1],[1],[1]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 4×4 matrix and the second is a 4×1 column vector. The resulting matrix will be a 4×1 column vector.

2. Calculate the first entry by taking the dot product of the first row and the column vector.

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

3. Calculate the second entry by taking the dot product of the second row and the column vector.

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

4. Calculate the third entry by taking the dot product of the third row and the column vector.

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

5. Calculate the fourth entry by taking the dot product of the fourth row and the column vector.

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

6. Assemble the results into the final column vector.

Final Answer

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

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