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Differential Equations and Linear Algebra (4th Edition)
- Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).arrow_forwardLet B = R − {3}. Define g : B → B by g(t) = 3t/(t − 3)Show that the function g is surjective. Note: R is the set of real numbers.arrow_forwardDetermine whether the function f : R → R given by f (x) = 4x + 6 is a bijective function.arrow_forward
- Let F = Q, s(x) = x² + 1, and E = Q[r]/(x² + 1)Q[x]. i) Factor the polynomial x? +1 € Q[x] into linear terms in E. ii) Show that the polynomial r³ – 1 € Q[x] only has a single root in E.arrow_forwardThe function f:C→C defined by f (z) = e² +e² has (a) Finitely many zeros (b) No zeros (c) Only real zeros (d) Has infinitely may zerosarrow_forwardConsider the linear operator T:R3→R3, given by T(v)=A⋅v, where [image]:What is the minimal polynomial of T? Choose an option: a) mT(x)=x(x−1)2. b) mT(x)=(x−1)2. c) mT(x)=(x+1)(x−1)2. d) mT(x)=(x+1)2. e) mT(x)=(x+1)(x−1).arrow_forward
- Let A = B = C= {x|x is a real number). Let f : A → B and g : B → C be defined as follows: f(a) = 6a + land g(b) = b³ Compute the following: (a) (f o g)(2) (b)(g o f)(2) (c) (g o f)(x) (d) (ƒ o g)(x) (e) (ƒ o f)(y) () (g o g)(y)arrow_forwardShow that the function f : R – {3} → R – {5} defined by f(x) = *, is bijective and determine f-(x) for x eR – {5}.arrow_forward
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