Linear Algebra

-----------------------

Question 1 Suppose (x1.X2) + (y1. yz) is defined to be (x1 + yz.x2 + )I). With the usual multiplication ex = (cx1. cx2), which of the eight conditions are not satisfied? 2 Suppose the multiplication ex is defined to produce (cx1. 0) instead of (cx1. cx2). With the usual addition in R2, are the eight conditions satisfied? ()xty=)+x (2) x + (y + = ) = (x+y)+: (3) There is a unique "zero vector" such that x + 0 = x for all x (4) For each x there is a unique vector -x such that x + (-x) = 0 (5) 1 times x equals x (6) (CIC2)x = CI(C2x) (7) c(x + y) = ex +cy (8) (C1 + c2) x = cix + czx. For Question 1 and 2, check whether eight rules are satisfied or not; and explain why