Simplify the Matrix [[3/11,-4/11],[-5/11,3/11]][[-2],[4]]

Problem

[[3/11,−4/11],[−5/11,3/11]]*[[−2],[4]]

Solution

1. Identify the dimensions of the matrices to ensure multiplication is possible. The first matrix is 2×2 and the second is 2×1 resulting in a 2×1 matrix.

2. Multiply the first row of the matrix by the column vector.

3/11*(−2)+(−4/11)*(4)

3. Multiply the second row of the matrix by the column vector.

−5/11*(−2)+3/11*(4)

4. Calculate the sum for the first entry.

−6/11−16/11=−22/11

5. Calculate the sum for the second entry.

10/11+12/11=22/11

6. Simplify the resulting fractions to integers.

−22/11=−2

22/11=2

Final Answer

[[3/11,−4/11],[−5/11,3/11]]*[[−2],[4]]=[[−2],[2]]

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