Multiply the Matrices [[-1,1],[0,1]][[1],[4]]

Problem

[[−1,1],[0,1]]*[[1],[4]]

Solution

1. Identify the dimensions of the matrices to ensure they can be multiplied. The first matrix is 2×2 and the second is 2×1 so the resulting matrix will be 2×1

2. Calculate the first element of the result by taking the dot product of the first row of the left matrix and the column of the right matrix.

(−1)*(1)+(1)*(4)=−1+4=3

3. Calculate the second element of the result by taking the dot product of the second row of the left matrix and the column of the right matrix.

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

4. Combine the results into a single column matrix.

[[3],[4]]

Final Answer

[[−1,1],[0,1]]*[[1],[4]]=[[3],[4]]

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