2. Prove the following result using the definition of subspace: Let (V,+,-) be a vector space over R and WCV. Suppose that i) W + Ø; and ii) For every w, u EW and every k, meR, ku+mwW. Then Wis a subspace of V.

Q: A = = || we ๆๆ -2 0 1 4 B = - 3 2 Ho - o blo

A: We have to find the matrix

Q: The sum of two numbers is 44 . The larger number minus the smaller number is 2 . Use the…

A: To solve the following problem

Q: In a vector space V , prove that 0v = 0 for all v ∈ V

A: In this question, we want to prove that for a vector space V , 0v=0 for all v in V.

Q: A set of three scores consists of the values 2, 5, and 8. E3X - 1 = ΣΧ2 - 1 = Hint: Remember to…

A: E3X -1  EX2 -1  which of this consist 2,5,8  here for this we put value in both equation and see if…

Q: 6(3z-2)+1/2(18z-22)=2(-6z-3)+3z+7

A: …

Q: The function f(x) = 487(5)* represents the growth of a ladybug population every year in a wooded…

A:

Q: A lamp costs the store $56 and sells the lamp for $89. Find the rate of markup based on cost. Round…

A: On solving this we will get

Q: √x - 1)(√x + 1)   ^ is this a polynomial? pls explain

A:

Q: candy manufacturer makes 7 kinds of brown chocolate candies and 4 kinds of white chocolate candies.…

A:

Q: Describe the zeros of the graphed function. ++ 6 M 4 10 O A The function has three distinct real…

A: This question is related to graph of functions, we will solve it using given information.

Q: A light is placed on the ground 4 feet from a point on the path leading up to a building. The light…

A: Concept: First using the given information formation of the diagram Similar triangle: Triangles of…

Q: Which graph shows f (x) = 4-2 and its translation g(x) = f(x) +7? O O

A:

Q: Solve the following system of equations. √ x² + y² = 29 x-y²= -9

A:

Q: A mirror should be centered on a wall. The mirror is 36 inches wide and the wall is 18 feet wide.…

A:

Q: Ben earns $9 per hour and $6 for each delivery he makes. He wants to earn more than 155 in an 8 hour…

A:

Q: 5. For which value of x do the following vectors form a linearly dependent set in R³ m=(x + x=(₁…

A:

Q: Graph the ellipse. (x + 2)² (y + 2)² =1 + 25 16

A: The ellipse can be graphed as below.

Q: Solve the following differential equation. y" +4y' + 4y = xe¯x

A:

Q: Use the graph of f(x) = |x| to write an equation for the function represented by each graph. (a) y X…

A: This question can be solved using the horizontal and vertical shift concept of the graphs.

Q: Question Show that w= [(a,0, b)la, bεR] is a subspace OF R³

A:

Q: 1.What is the smallest number that can be exactly divided by 2, 3, 4, 5  and 8 ? 2.What are the…

A: To answer the given questions.

Q: Choose the polynomial function that corresponds to the given graph. -B A ƒ (x) = −x(x − A)²(x + B)³…

A: From the given polynomial graph, we have to find its equation.

Q: (a) Let u, v and w be nonzero vectors in R³. If u and v are each orthogonal to w, then 2u3v is…

A:

Q: 1. A man walked along a straight level path toward a building. At one point the angle of elevation…

A: Since, you have asked multiple questions so we will solve first question for you.

Q: The Ylaya Textile Mill produces denim. The fixed monthly cost is $21,000, and the 2. variable cost…

A: Given Fixed Cost FC=21000                    variable V=0.45          selling price…

Q: +

A: We will find x.

Q: 1. Find the cofactor of 6 in matrix D 9 8 4 7 -9 3 D= -3 9 6 (8 2432 23 2

A: The cofactor  Aij of aij is defined by  : Aij =(-1)i+j det Mij .

Q: ich two equations represent a hyperbola? ect from the equations below. A 2-4-1 B C 81 D +2=1 36 2 36…

A: We have to find the hyperbola equation

Q: 3. If the terminal arm of angle 0, in standard position, passes through point (-b, 2b), where b>0,…

A:

Q: 4. For the following polynomial write the polynomial in standard form and specify: a) its degree b)…

A: Expand the polynomial then answer the questions.

Q: Use graphical approximation techniques to answer the question. When would an ordinary annuity…

A: Let x represent the number of years.  Hence,  Amount by simple intrest  => S=6100(1 + 0.05x)…

Q: Prove that (A + B)² = -(A + B) in matrix..

A:

Q: cant figure this one out

A: Solve the following

Q: Evaluate each determinant.

A: A = -1523

Q: Question 2 The owner of an apartment building can rent all 60 suites (i) if $120 per month is…

A: Number of suits for rent = 60  Charge for each suite = $ 120

Q: Solve the following equation for values of 0 between 0 and 360° [Hint: Express (3 sin 0 + 4 cos 0)…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Find the maximum value and the minimum value of the function and the values of x and y for which…

A:

Q: Factor by grouping (sometimes called the ac-method). 5x² +12x+4 First, choose a form with…

A:

Q: Determine whether the set {P1, P2, P3} is linearly independent in P2, where p₁ = 2 + x + 3x² + 4x³,…

A: Here, to check the elements of P2 are linearly independent or not. For that, let…

Q: I. Simplify. Write "undefined" for expressions that are undefined. 2 4 4 1.) -6 1 -3 -5

A: To simplify the given expressions.To write "undefined" for the expressions that are…

Q: Let f(x) = √20- x and g(x) = x² - x. Then the domain of fo g is equal to

A:

Q: GIVEN THE FOLLOWING MATRICES 3 A = B = 0 4 FIND THE FOLLOWING a) D + AB b) det (D) c) adj (D) 5 D= 3…

A: Given, A=13-43-2014B=-32725216133116D=31-250-4-453

Q: Let V be a vector space and let u, v E V. If W = {au + Bula, BE R}, prove that W is a subspace of V.

A: Given :W be the non empty subset of V satisfying conditions α,β∈R and αu+βv∈W

Q: 253. Find the distance between point A(-3, 1, 1) and the line of symmetric equations x=-y=-z.

A: Let B(a,b,c) be a point on a given line with direction vector v⇀=(x,y,z). Then distance of  a point…

Q: + -7 -6 -5 -4 y = 5 4 3 2 1 41 -2 -3 -4 -5 1 2 3 4 I 5 6 7 Q

A:

Q: Factor out the GCF from the polynomial. 25x -50y + 25 25x-50y + 25 = (Type your answer in facto

A: We have to find out the gcf

Q: Find the missing value that makes the following a factorable trinomial. Explain the process you used…

A:

Q: Kulvir's sales last week were $31 more than five times Stuart's sales. If together their sales…

A: First we will suppose stuart's sale then we will find kulvir's sale Then by total sale we calculate…

Q: Which equation represents the hyperbola graphed below? 10 2-2=1 A 5-8-1 B 3-1 C -4-1

A: Explained below

Q: Step 3

A: Solve the following