Simplify the Matrix

Problem

[[1,0],[0,0]]*[[1/2,−√(,3)/2],[√(,3)/2,1/2]]*[[a],[b]]

Solution

1. Multiply the first two matrices by calculating the dot product of the rows of the first matrix with the columns of the second matrix.

[[1,0],[0,0]]*[[1/2,−√(,3)/2],[√(,3)/2,1/2]]=[[(1)*(1/2)+(0)*(√(,3)/2),(1)*(−√(,3)/2)+(0)*(1/2)],[(0)*(1/2)+(0)*(√(,3)/2),(0)*(−√(,3)/2)+(0)*(1/2)]]

2. Simplify the resulting 2×2 matrix.

[[1/2,−√(,3)/2],[0,0]]

3. Multiply this result by the column vector [[a],[b]]

[[1/2,−√(,3)/2],[0,0]]*[[a],[b]]=[[(1/2)*(a)+(−√(,3)/2)*(b)],[(0)*(a)+(0)*(b)]]

4. Simplify the final vector components.

[[(a−b√(,3))/2],[0]]

Final Answer

[[1,0],[0,0]]*[[1/2,−√(,3)/2],[√(,3)/2,1/2]]*[[a],[b]]=[[(a−b√(,3))/2],[0]]

Want more problems? Check here!