1.21 Decide whether each subset of R3 is linearly dependent or linearly indepe: dent. 4 (b) { | 7 7, (c) { (a) { | –3 -4 } 7)} | } 5 14

Q: (e) Let A = {1,2, (3,4,5)), B=(2, 3, 4, 5, 6, 7). Find i. An B. A x B. P(AB), where P(X) is the…

A: According to the Bartleby guidelines I am answering only one first 3 parts.   We are given…

Q: .If X&Y are independent R.V's,what are the values of Var(X₁+X₂)and Var(X₁-X₂)

A: Solution X1 and X2 are independent random variables then Cov(X1,X2)= Then Var(X1+X2)=Var(X1)+Var(X2)

Q: 12. Consider the algebraic expression E = (X + 3Y)*(a – 2b) draw a tree according to the equation!

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Q: 2. Let f(x) = x - 5 and g(x) = x² +3x. a) Find (f + g)(x) b) Find (f – g)(x) c) Find (f g)(x) d)…

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Q: How many individual simple functions make up the following composite input? 2 1 5 6 A) 4 в) 5 c) 6…

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Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another…

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two…

Q: et f = xi+ yj + zk and g = |f|. Then Ve9 =

A:

Q: Determine if 0 >=(61-6-J-RA) is in the span of = 0

A: Given: -1225 To check:If -1225 is in the span of Φ=1100, 1001, 0110, 0011 or not.

Q: Find the GCF of -3x3 + 15x² – 6x

A: To find the GCF of -3x3+15x2-6x

Q: Suppose s and t are distinct natural numbers. Show that lcm(s, t) + lcm(s+1, t+1) > 2st/(sqr(|s −…

A: Given: s and t are distinct natural numbersTo prove: lcm(s, t)+lcm(s+1, t+1)>2sts-t

Q: each complex Let f be the map semaing nu mbes 2→X y show that flzi2)= f(2)fLZ).

A: The detailed solution is as follows below :

Q: 4. R= {(x,y) x + y ≤ 8} reflexive irreflexive symmetric asymmetric anti- symmetric 1. 2. 3. 4. Which…

A:

Q: 13. The function k is given by k(x) = (2x+1)(4x-7). Find the x-coordinate(s) of all critical…

A: Critical points are points where the derivative of the function is 0 or undefined. To find the…

Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

A:

Q: If A has a row or column consisting entirely of zeros, then Select one: a. A is nonsingular b. A is…

A: Given: A is row or column consisting entirely of zeros .

Q: In S, if T-{(G { G {), them r ) is In S, if T-1(G )G 2 3 \1 2 3 2 3 }, then 3 1 2 3 2 3

A:

Q: Using the information in the table below, find the occupancy rate for the years 2021 to 2024 using…

A: Given α=0.3. Let At represent the actual values of the occupancy rate and Ft represent the forecast…

Q: Find the value of a for which U = a 1 10 is in the set 0 -1 3 0 H = span 5 3 -1 2 -2 -2 a =

A: The value of a=-7 .Explanation:Step 1: Step 2: Step 3: Step 4:

Q: EXERCISES 4.1 Which elements of (Z₁0, ). are contained in ?

A:

Q: 5.4 Find the least square regresion line for the data pint. (let * be the în de pendent vamiable and…

A: Given data point is (-1,3),(1,1)(3,0)

Q: 3 I- 0) = [u- w -3 [-1 4] 6.

A: We will solve it in parts Consider 0-1453-101-1 = (0)(5)+(-1)(-1)+(4)(1)    (0)(3)+(-1)(0)+(4)(-1)=…

Q: Let 13 20 x 20+ y = 2 be the equation of a curve in the xy-plane. Find the equation y = T(x) of the…

A:

Q: 1. State the properties of the Bassel function.

A: Here are some properties of Bassels Function

Q: O Is the set S=\[1.2], [-4 2. abaris for R?.

A: We know dimension of ℝ2  is 2  this implies basis of ℝ2 contains two linearly independent vectors.…

Q: a PDE from the following- @u =f() Form メソ

A: We eliminate the arbitrary function f from the given equation to form the required partial…

Q: Suppose that P(A) = 0.4, P(B) = 0.3 and PAUB)-042, then a. A and B are dependent b. none of the…

A: We have to find out correct answer...

Q: Refer to B={ ={₁0, -6, 0.23, 3, -1.7, √7}. Determine which elements belong to the given set.…

A:

Q: Show that if we make the change of variables =x – ct and n =x + ct, then, as in (16.7), a?u ,a²u a…

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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: Let A {a, b} and B = {1, 2}. Give an element of A x B x A.

A: Let M and N be two sets. The Cartesian product, M×N is the set of all possible ordered pairs with…

Q: 10. S = {r² + 3r + 1,2r² + x – 1, 4r + 1} is: %3D a. a linearly independent set of P2. b. a linearly…

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Q: A. B. f(x) f(x) -3 3 -2 4 3 4 -1 4 1 6 2 C. D. f(x) f(x) 3 -1 3 3. 4. 5 3 6. 3 Which table does NOT…

A: for a valid function for one value of x, the function could not be more than one vale or having only…

Q: a. If g(x) = 2x - 1, find g(8) and g(- 8). b. Find the image of 5. c. Find the preimage of 7.

A: To determine: a) If gx=2x-1, find g8& g-8 b) Find the image of 5. c) Find the preimage of 7.