a. Let _ be the line spanned by _ cos sin . Show that the standard matrix for R_ is R = _ cos 2 sin 2 sin 2 cos 2 by using Figure 2.10 and basic geometry to find the reflections of (1, 0) and (0, 1). FIGURE 2.10 _ b. Derive this formula for R by using R_ = 2P_ I (see Example 3). c. Letting A be the rotation matrix defined on p. 98, check that A2 _ 1 0 0 1 = R = A _ 1 0 0 1 A(). d. Give geometric interpretations of these equalities.

Week 10 Section 6.3 §6.3Confidence Interval for When x is Normally Distributed, n is Small and Unknown Theorem: Suppose x is a normally distributed random variable. Suppose a SRS of size n 2 is obtained. Then the 1 confidence interval for the mean value of x is given as - xx= sample mean value. - s =sample standard deviation - n = sample...