Final answer:
Orthogonal matrices in R2 are 2x2 matrices with orthogonal unit column vectors.
Step-by-step explanation:
An orthogonal matrix in R2 is a 2x2 matrix whose columns are orthogonal unit vectors. In other words, the dot product of any two columns of the matrix is zero, indicating that the vectors are perpendicular to each other. Additionally, the magnitude of each column vector is equal to 1, signifying that they are unit vectors.
For example, the matrix [cos(q), -sin(q); sin(q), cos(q)] is an orthogonal matrix in R2, where q is any angle. The first column [cos(q), sin(q)] and the second column [-sin(q), cos(q)] are orthogonal vectors that form an angle of q.