.
(a) (2,1)T;
(c) (1.6,0.6,1.2)T
.
(1a) p=(3,1,0)T,r=(0,0,2)T
(1c) p=(3.4,0.2,0.6,2.8)T,
r=(0.6,−0.2,0.4,−0.8)T
.
(a) {(1−2α,α)T∣∣α real};
(b) {(2−2α,1−α,α)T∣∣α real}
.
(a) p=(1,2,−1)T,b−p=(2,0,2)T;
(b) p=(3,1,4)T,p−b=(−5,−1,4)T
.
(a) y=1.8+2.9x
. 0.55+1.65x+1.25x2
.
(a) Hint: If b∈R(a) then b =Ax for some x∈Rn.
(b) Hint: R(A)⊥=N(AT).
10. Hint: If the case of a consistent system, what can we conclude about b in relation to one of the fundamental subspaces?
14. The least squares circle will have center (0.58,−0.64) and radius 2.73 (answers rounded to two decimal places).
15.
(a) w=(0.1995,0.2599,0.3412,0.1995)T
(b) r=(0.2605,0.2337,0.2850,0.2208)T
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