Add [[5,2],[2,2]][[2],[6]]

Problem

[[5,2],[2,2]]*[[2],[6]]

Solution

1. Identify the operation as matrix multiplication between a 2×2 matrix and a 2×1 column vector.

2. Multiply the first row of the matrix by the column vector by calculating the sum of the products of corresponding entries.

5*(2)+2*(6)

3. Calculate the value for the first entry of the resulting vector.

10+12=22

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

2*(2)+2*(6)

5. Calculate the value for the second entry of the resulting vector.

4+12=16

6. Combine the results into a new 2×1 vector.

Final Answer

[[5,2],[2,2]]*[[2],[6]]=[[22],[16]]

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