Please explain how to solve step by step and name any rules or theorems used.

The following is from Chiang's fundamental mathematical economics.

2 1. Given A = [ 6 ; ].8=[; 2 ]. and c =[: ;]. find: (0) A + B (b) C- A (C) 3A (d) 48+ 20 2. Given A = 3 8 . 6 -[3 8]-and bx 2. Given w = 2 .x= ].>=.andz =] (a) Which of the following are defined: w'x, xy', xy', y'y. zz', yw', x - y? (b) Find all the products that are defined. 3. Having sold n items of merchandise at quantities Q1. .... Q, and prices P. .... P. how would you express the total revenue in (a) _ notation and (b) vector notation? 4. Given two nonzero vectors wj and w2, the angle s (0" so s 180 ) they form is related to the scalar product w,wz (= w,wj ) as follows: acute e is a(n) right angle if and only if w, wz = obtuse Verify this by computing the scalar product for each of the following pair of vectors (see Figs. 4.2 and 4.3): (0) m = 2 ."2 = [\\] ONO oo - (b) m = !].=] com-3.- (0) w - 3].2- [3] 5. Given u = |and v= , find the folowing graphically: (0) 2v ( C ) u - v (e) 2u + 3v (b) u -v (d) v -u (f) 4u - 2v