Multiply the Matrices

Problem

[[0,0],[−√(,3)/2,1/2]]*[[−2],[3]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 2×2 matrix and the second is a 2×1 matrix. The resulting matrix will be a 2×1 matrix.

2. Calculate the first element of the resulting matrix by taking the dot product of the first row of the first matrix and the column of the second matrix.

0*(−2)+0*(3)=0

3. Calculate the second element of the resulting matrix by taking the dot product of the second row of the first matrix and the column of the second matrix.

−√(,3)/2*(−2)+1/2*(3)

4. Simplify the expression for the second element.

√(,3)+3/2

Final Answer

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

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