Section 2.1: 1(b,d,f), 2(b,d), 8, 10

Section 2.2: 2(d,f), 4(b), 13, 15

Section 2.3: 1(b,d), 2(a), 5(b,d)

Review Exercise (not from the textbook): Let a and b be nonzero vectors in \( \mathbb{R}^n \). Show that \( \mathbf{c}:= \operatorname{proj}_{\mathbf{a}}\mathbf{b} \) is the closest vector to b out of all the vectors parallel to a, i.e. show that \( \| \operatorname{proj}_{\mathbf{a}}\mathbf{b} - \mathbf{b}\| \le \| t\mathbf{a}-\mathbf{b} \| \) holds for all \( t\in\mathbb{R} \). (Hint: square the norms and expand in terms of dot products, and differentiate, or cite facts about quadratic polynomials.)