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- graph'the Sorution to the follow imy inginequratityon animber line nur (x-2) (x+5) z OIf l is a line through (0,0), the point (0,0) divides the line l into two rays. Also, a complex-valued function g on a set S is said to be bounded if there is some finite M such that |g| < M on the set S. So we need to find out for which rays through the origin does e^z satisfy this property.4. Consider -- -- *-H = = V3-1 2 k a) For what values of k is v3 in Span {V₁, V₂}? Explain. b) For what values of k is {v₁, v2, V3} linearly dependent? Explain. [-51 6 0
- Let T: R³ R² be defined by T (E) 2x1 -2x2 + x3 Ex: 5 +2₂] -3 ---(~- -[:] ·~ -E] ·~ -E] --²-(~- -|*|·- -|A|]} [5], = [5]} Let Bu₁ = {" = -6 113 and C V1 = V₂ 0 5 What augmented matrix should be used to find [7], the matrix representation of Twith respect to the bases B and C.For each situation, find degree of freedom (d. f .), numerator, denominator, tobtained, and area under the curve (AUC) beyond tcritical, and fill out the empty cells.a) Prove the one point rule - 3-version: (3x)(x = t ^ A) = A[x := t] if x is not free in t. b) Prove the dual result 6 on p.176. Prove (3x) AvBC = (3x) ÂС V (3x) BC. (Hint: Translate first to Standard notation) c) Prove using the auxiliary variable metatheorem: + (3x) (A → B) → (Vx)A → (3x)B