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

Problem

[[2,−1],[1,1]]*[[4],[5]]

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 entry of the product by taking the dot product of the first row of the left matrix and the column of the right matrix.

(2)*(4)+(−1)*(5)

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

(1)*(4)+(1)*(5)

4. Simplify the arithmetic for each entry.

8−5=3

4+5=9

Final Answer

[[2,−1],[1,1]]*[[4],[5]]=[[3],[9]]

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