2. Determine which of the following statements are true and justify each conclusion. Assume that T...
Problem 7. (20 pts) For each of the ten sentences below, justify whether they are true or false. If true, you must provide a proof, if false you must provide a counter-example. (a) The linear map ƒ : R² → R² defined by (:)-()) is an isometry. (b) Any linear map f : R² → R² of the form (;)-( :)(;). with a + 0, must be an isometry. (c) The composition fog : R² → R? of two isometries...
6. Justify briefly (max two lines) if the following statements are true or false. Answers with just Tor F won't receive any points. (a) (1 point) The curve with vector (Cartesian) equation r(t) = (t cost, tsint, t) lies on the surface with cylindrical equation 2 = 72 (b) (1 point) If ñ x p=0 then ñ = 0 or p=0. (c) (1 point) 24 – 4y2 lim (x,y)+(0,0) 22 + 2y2 = 0 (d) (1 point) If f(x, y)...
5. Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation S on R given by xSy if and only if X – Y E R – N is an equivalence relation.
Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation Son R given by Sy if and only if 1 - YER - N is an equivalence relation. (b) The groups (R,+) and (0,0), :) are isomorphic.
Answer Save the vectors are any non-zero vectors Determine ir the following statements are True or False. Assume )M (b) The intersection of Z = (x2+4)cosy + 9xy and the plane, y-r, is a parabola. (c) The vectors 47- 97+20k and 87- 187-40k are parallel. (d) The graph of fix.) = x2 + r2 is a circle. (e) The spacing of the contours of a function of 2 variables given by y 3x2+C2 will increase as C increases. Answer Save...
am i correct? Select ALL TRUE statements. For the given AABCand points L, M, and N that are the points at which the incircle touches the sides BC, AC, and AB respectively, the lines AL, BM, and CN are concurrent. Bisector of an interior angle of a triangle and the bisectors of the remote exterior angles are concurrent. A proper Cevian line contains any two points of the given triangle ABC. The interior angle bisectors of an acute triangle are...
4. True or False. Label each of the following statements as true or false. If true, give a proof, if false, give a counterexample. (a) Every nontrivial subgroup of Q* contains some positive and some negative numbers (b) Let G be a finite group. Let a E G. If o(a) 5, then o(a1) 5. (c) Let G be a group and H a normal subgroup of G. If G is cyclic, then G/H is also cyclic. (d) Le t R...
question about linear algebra 21. The following two lines := -i+j+ k + t(2i - 2j - 2k), t e R r and y2 1 = 2 -1 intersect each other. What is the equation of the line (where s E R) passing through the intersection point of these two lines and perpendicular to both of them? r -ijk s(i - j - k) (a) (b) r i2j+3k + s(i - 2j + 7k) (c) (d) rsik) (e) =j-k s(i...
4.) NSTRUCTIONS: Select the conclusion that follows in a single step from the given premises. Given the following premises: 1. ∼M ⊃ S 2. ∼M 3. (M ∨ H) ∨ ∼S a. M ∨ H 3, Simp b. M ∨ (H ∨ ∼S) 3, Assoc c. ∼S 1, 2, MP d. ∼ M ∨ S 1, Impl e. H 2, 3, DS 3.) NSTRUCTIONS: Select the conclusion that follows in a single step from the given premises. Given the following...
Desargues' Theorem . Modern Geometry B 7 B In the picture above, triangle AABC and triangle AA'B'C' are perspective from the point X, where A' and C' are points at infinity not indicated in the picture, so this problem involves working in the projective plane. The lines XẢ and B’Ś are parallel in the affine plane (that is, they intersect at a point at infinity in the projective plane), and V is on B'Ś. The lines XĆ and B'R are...