Question: please show all the details Problem 5 (20 points): Consider the 2 x 2 orthogonal matrices S Co F S wher c = cos(0) and

please show all the details

Problem 5 (20 points): Consider the 2 x 2 orthogonal matrices S Co F S wher c = cos(0) and s = sin(0) for some 0. The first matrix has detF = -1 and is a reflector (the special case of a Householder reflector in dimension 2). The second has detJ = 1 and effects a rotation instead of reflection. Such a matrix is called a Givens rotation. Describe exactly what geometric effects left-multiplications by F and J have on the plane R". ( J rotates the plane by the angle 0, for example, but is the rotation clockwise or counterclockwise?)

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