Determinant of a map/ endomorphism is nothing but the determinant of its associated matrix.
Here the associated matrix is M.
So det(T)= det(M)= ac-0b= ac.
So answer is ac. ( a multiply c).
(8) Let TC C(R111) be defined by rar' t br + c)-(2a b)z? t (2b α-c) r + c b (a) Find M(T) :-M(T, B. B) where B-(z2, 1, 1} (b) Compute det(M(T). Is Tinvertible? e) If possible, write an explieit formmla for T (az2 b c). (8) Let TC C(R111) be defined by rar' t br + c)-(2a b)z? t (2b α-c) r + c b (a) Find M(T) :-M(T, B. B) where B-(z2, 1, 1} (b) Compute det(M(T)....
• Let V be a 2-dimensional real vector space, and let T E End(V). Show that T is diagonalizable over C but not over R if and only if tr(T)2 < 4. det(T).
equivalent 4. Let E C R. Prove that the following statements are (a) E is Lebesgue measurable (b) Given e> 0, there exist m* denotes the Lebesgue measure of a set (c) Given e 0, there exist a closed set F such that F C E and m* (E- F) < E. (d) There exists a set G (a countable intersection of open sets) such that E C G and m* (G - E) 0 (e) There exists a set...
equivalent 4. Let E C R. Prove that the following statements are (a) E is Lebesgue measurable (b) Given e> 0, there exist m* denotes the Lebesgue measure of a set (c) Given e 0, there exist a closed set F such that F C E and m* (E- F) < E. (d) There exists a set G (a countable intersection of open sets) such that E C G and m* (G - E) 0 (e) There exists a set...
equivalent 4. Let E C R. Prove that the following statements are (a) E is Lebesgue measurable (b) Given e> 0, there exist m* denotes the Lebesgue measure of a set (c) Given e 0, there exist a closed set F such that F C E and m* (E- F) < E. (d) There exists a set G (a countable intersection of open sets) such that E C G and m* (G - E) 0 (e) There exists a set...
Let f : R2 → R be a uniformly continuous function and assume that If(y,t)| M. Let yo E R. The goal of this exercise is to show the existence of a function φ : [0, 1] → R that solves the initial value problem o'(t)-F(d(t),t), ф(0)-Yo (a) Show that there is a function n1,R that satisfies t <0 n(リーレ0+.GF(du(s-1/n),s)ds, t20. Hint: Define фп first on [-1,0] , then define фп。n [0,1 /n), then on [1/n, 2/n], and so on...
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(8) Given a C1-function f : Rn->M, let M (x, z) E R#x R | z- f(x)) be the graph of f. Let TpM denote the tangent space to M at a point p = (xo, 20) E M. Find TİM and compute its dimension. Hint: draw a picture.
t2s points). Let B(t) be Brownian motion and let zu) with drift u0. For any B()+ ut be Brownian motion t 0, let T be the first time Z(t) hits a. a) Show that T, is a random time for Z(t) and for B(t). b) Show P(T, 0o)1. c) Use martingale methods to compute E [e-m] for any θ > 0 r> t2s points). Let B(t) be Brownian motion and let zu) with drift u0. For any B()+ ut be...