The following facts can be proven 1 An orthogonal 2 x 2

Last updated: 4/9/2023

The following facts can be proven 1 An orthogonal 2 x 2 matrix must have the form where 2 Every orthogonal 2 x 2 matrix is of the form or is a unit vector 2 sin 0 cos 0 2 3 or where 0 0 2m 3 An orthogonal 2 x 2 matrix Q corresponds to a rotation in R if det Q 1 and a reflection in R2 if det Q 1 sin 0 cos 0 Use the above facts to determine whether the given orthogonal matrix represents a rotation or a reflection Orotation O reflection If it is a rotation give the angle of rotation If it is a reflection give the line of reflection Enter the angle if it is a rotation Enter an equation involving x and y if it is