9. Show that F= field? T a b a | a, b € Z5 is a subring of M2(Z5). Is Fa be Z5

Q: evaluate the Pirst and second deriugive of f) = 327+5csin 3x• %3D at x= 11 , 2.5 &3.7

A: To evaluate the first and second derivatives of f(x)

Q: 31. Let f(x) = [x²/3]. Find f(S) if a) S= (-2,-1, 0, 1, 2, 3). b) S = {0, 1, 2, 3, 4, 5). c) S = {1,…

A: The given function is, fx=⌊x2/3⌋. To Find: f(S) for the following set S, (a) S=-2,-1,0,1,2,3 (b)…

Q: 25. f(x) =x-16x A) -4, 0, 4 B) -8, 0, 8 C) -2, 1, 2 D) 2, 4, 8 26. g(x) = x* -x' -6 A) -V3,-V2, 2, 3…

A:

Q: 18. Determine whether each of these functions is a bijec- tion from R to R. a) f(x) = -3x + 4 b)…

A: As per guidelines, we will solve first three subparts of the question. a) Given function is fx=-3x+4…

Q: Prove that 1 1 16 ≤ (a+b+c+d) = + = + b + ax (²=²+ + + + + + + ² + 1 = 0) d for all positive numbers…

A:

Q: а. v(Ã ·) = Ã × (V x B) + B x (v x Ä) + (Ã ·v)Ē + (B · V)Ā b. · (Ã × B) = B · (v × Ã) – Ã · (V × B)…

A: Part(a): ∇A⇀·B⇀=A⇀×∇×B⇀+B⇀×∇×A⇀+A⇀·∇B⇀+B⇀·∇A⇀ From the left-hand side of the given equation,…

Q: x, y, z)=x²√√x - y² - z²

A:

Q: Prove that if x, y € R, x > 0 and y > 0, then √√√x+y√√x + √y.

A:

Q: Consider the interpolating polynomial for f(x) = x³ based on th points (0,0), (1,1) and (2,8). Find…

A:

Q: Are u sure its not 1

A: It is given that a=0 and b=1.

Q: Suppose that the translation T is described by (?,?)→(?+2,?−1)(x,y)→(x+2,y−1). What translation…

A: We have to find the translation described in x,y→x+2,y-1.

Q: Show that the function (, -): R² × R? → R defined by setting = 1122+ 2x12 + 2y172 + 8y142 = is an…

A:

Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

A:

Q: AN 3. Given R(x) = a) R (-1 3x-1 TED COMPILED ANDEDIB COMPILED AND EDITE COMPILED AND SoCOMPILED AND…

A: This is a composition of functions.

Q: Find the degree of Q(V2, V5) over Q.

A:

Q: Justify wether the following is an inner product or not =5x1y1-x1y2-x2y1+2x2y2 where x=(x1,x1) and…

A: By using axioms of inner product we have to show whether <x, y> is an inner product or not.

Q: Determine whether the function defined by = 2x1y₁ - x1y2 - x2y1 + 2x2y2 is an inner product on R².

A:

Q: 1. Determine whether each of these functions is a bijection from R to R a) f (x) = 5x + 10 B) f (x)…

A:

Q: Let u = = (–3, 3, 5) and v = (−6, −4, −7). Compute the following: ū X x v = v × x ū x ū ū=

A: Please note that as per bartleby guidelines, we need to answer only the first three sub-parts.Kindly…

Q: Let X = the integers. Let Y = {0, 1, 2, 3, 4, 5}. %3D Let f : X Y be defined as the remainder when x…

A:

Q: 6. Let ao, a1, a2, a3, a4 be constant real numbers such that a1 a2 a3 + + + + a4 = 0. 5 4 3 2 Show…

A: Our objective is given below:

Q: Gue Functions fandg, FindCa) Cf g) C&) and its dlomiain, and b) (g oF (x) and its. O F(x)--6xtq,…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Let us define a. Verify that f(x, y) = af ду xy(x² - y²) x² + y² af y(x² - y² + 4x²y²) əx (x² +…

A:

Q: Qu6. Consider the polynomial below in which we have a parameter z. Q(x)=x³+(2-5)x² + (2+1)x+…

A: Given that a polynomial Q(x) with a parameter z  Q(x)=x3+(z-5)x2+(z+1)x+(11-3z) We need to find set…

Q: 3. Construct a bijection f: [0, 1] → (0, 1) UN.

A:

Q: (1) if is reflexive, symmetric, or transitive. For a, b = Z, define ab if a + b is a multiple of 3.…

A: A relation is a subset of the cartesian product A×B where A and B are non-empty sets. For cartesian…

Q: 17. Use Theorem 4.7 to prove that Vx + 3 2 V3 + x/4 for

A: Let,

Q: — 2х1 — 5х2 + 8хз x1+3x2 – 5x3 +x4 |3x1 + 11х2 — 19хз + 7x4 X +7x2 — 13хз + 5х4 x1 X2 . Let T X3 X4…

A: The given transformation T can be written as            Tx1x2x3x4=-2-58013-51311-19717-135x1x2x3x4is…

Q: Let fi = 1+x + x² + x³ , f2 = 1 + 2x + 3x? + 6x³, f3 = 3+2x + ? + 5x4, and g = 1+x + 2a? + tæ³. For…

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Q: 6. Show that there is a one-to-one correspondence between the Cartesian products A x B x C and A x…

A:

Q: 1. Multiply. x' x x a. 5x'z x- 2xz2 - 4xy x-3x'yz g. 2a'b'c x 2abcd C. e. of

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: h. By completing the square, re-express fx,y (x, y) in the form fx,y(x, y) = e-(ax-by)² e-cy², Where…

A: Suppose X and Y are jointly distributed with pdf  where .