Question 3. Suppose n > 1, and let Un = {xg(x) : g(x) E Pn-1}. Is Un a subspace of P,? If yes, prove it. If not, find a counter example. %3D

Q: Problem 3.24. Let X = [0, 1] U{2} C R. On the one hand, X has a subspace topology T1 induced by the…

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Q: Question 3 X1+2x2 -2x1-4x2 :X1, X2 real numbers is a subspace of R3. Then dim H = %3D %3D 3x1+6x2

A: Given H=x1+2x2-2x1-4x23x1+6x2

Q: Problem 1. Let W = {(x, y, z) e R³ : az = 0}. Is W a subspace of R³? Justify your answer.

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Q: QUESTION 6 and b= Let W=span ( - 1+x,1+x²) be the subspace of P₂ equipped with the evaluation inner…

A: let W=span-1+x , 1+x2 be the subspace of P2 if p=12+6x-12x2 then projwp=a+bx+cx2 find the value of a…

Q: - 15 - 13 -1 Let y = and v2 Find the distance from y to the subspace W of R“ spanned by v, and v2,…

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Q: 22.13 Suppose A =|1 2 and b=0 3 Compute x = (ATA)-'A*b, P= A(ATA)-A", and Ax Pb. What is the…

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Q: Question 4 4.1) Let W be the set of all matrices A € M22 such that Prove or disprove that W is a…

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Q: Question 3. Suppose n > 1, and let Un = {xg(x) : g(x) E Pn-1}. Is Un a subspace of P,? If yes, prove…

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Q: Problem 6. ing holds. Let W₁ and W₂ be subspaces of a vector space V. Show that the follow- W₁UW₂ is…

A: Given: W1 and W2 are subspaces of a vector space V. To show: W1∪W2 is subspace of V if and only if…

Q: QUESTION 2 Determine whether W = {(a, 2, b)|a, b = R} is a subspace of R³.

A: To determine whether W is a subspace or not.

Q: 1. Let W = {A E M„ (R): Tr(A) = 0}. Prove that W is a subspace of M„(R). Hint: Complete the…

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Q: Linear algebra

A: Consider the set

Q: QUESTION 5: The subspace of P, spanned by the polynomials 1+x+x², x+x²+x³, 1+x²+x³, 3 and 1+x+x³ has…

A: The objective of the question is determine the dimension of the subspace.

Q: Problem 8. points) Determine whether the given set S is a subspace of the vector space V. ? * 1. V =…

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Q: Question 2 Given the subset w =((1,1,3,1),(-1,3,1, -1).(3,- 1,1, - 1).(-1, -1,1,3) of R4, which of…

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Q: 4. Suppose A is 5 x 7, and Nul A has dimens (a) What is rank A? Explain how you de= your answer. (b)…

A: Given, A is 5×7, and Nul A has dimension 5.

Q: 2) One of the following subsets of IR2 is not subspace: a) S = {, xeR} b) s = {], = x3} %3D %3D e) s…

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Q: Question 3. Let (X,r) be a topological space and YCX. Show that if the subspace (Y,r,) is connected,…

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Q: Suppose that S, and S2 are nonzero subspaces, with S1 contained inside S2, and suppose that dim(S2)…

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Q: QUESTION 1 Show that W = {(a, 0, b)|a, b ∈ R} is a subspace of R 3

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

Q: Problem 7. Suppose a E R. Show that the set of contimuous real-valued functions f on the interval…

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Q: Problem 1 Find the distance d(v, W) from i = E R' to the subspace W = Span Hint: First check if W…

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Q: Question 2. Is the collection F of all polynomials p(x) with p(3) polynomials? = 0 a subspace of P,…

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Q: Problem 30. Let H be a Hilbert space and M be a closed subspace of H. Denoting by P: H – M the…

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Q: Find a basis for the following subspace of Rª over R: 3 1 4 7 span 10 11 13 What is the dimension of…

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Q: Suppose that S1 and S, are nonzero subspaces, with Si contained inside S2, and suppose that dim(S,)…

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Q: Question 2 Consider the following subspace of R given by V = {(x,y, z) E R | a + 2y + z = 0} a) Find…

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Q: 3.12. Show that for a subspace E we have (E-)- = E. Hint: It is easy to see that E is orthogonal to…

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Q: Problem 7. Suppose a ER. Show that the set of contimious real-valued functions f on the interval [0,…

A: Given α∈ℝ and W be the set of all continuous real valued functions f on interval 0,1 such that…

Q: -3 Find the orthogonal projection ŷ of y = -1 onto the subspace -2 5 W = Span { u1 = -5 u2 = -3 Ex:…

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Q: Problem 4. Explain whether or not the following sets are subspaces of the given vector space a+ (a)…

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Q: 5.) Find the dimension of the subspace of Rª spanned by 5 10 , and 15

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Q: 3 1 and x2 = -2 2. Let S be the subspace of Rª spanned by x1 = Find a basis for S-. 1

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Q: Question 9 Solve the problem. Let H = a + 3b + 4d c+d -3a-9b+ 4c - Sd -c-d Find the dimension of the…

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Q: Problem 3.2.1 Every vector space (V, R, +, .) has always two subspaces, namely the zero subspace {0}…

A: The statement "Every vector space V has always two subspaces, namely the zero subspace {0} and V…

Q: -4 - 1 - 2 and v, = - 1 1 Find the distance from y to the subspace W of R spanned by v, and v,,…

A: Given: y=3-1113,v1=1-2-12v2=-4103 and Closest point to y in W is y^=-1-5-39

Q: QUESTION 2 Determine whether W = {(a,2,b)la, b = R} is a subspace of R³.

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Q: Question 1 Let U = Span and W Span be subspaces of R³. Find bases for U +W and Un WW.

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Question 1. spa *are subspaces of R3 (vo

A: Given                       U = span(1,0,0), (1,3,4), (0,3,4)and      W =span(1,1,0), (1,1,-1),…

Q: Question 29 Let Py have the inner product given by evaluation at -3, -1, 1 and 3. Suppose that po…

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Q: lem 3. Suppose that S, and S, are nonzero subspaces, with S, contained inside S2, and suppose that…

A: Dimension of S2 =4  Dim(S1) <= dim(S2)  As S1 is non zero , so dim(S1) >0 So, dimension of S1…

Q: Question 15 Find a basis and the dimension for the following subspace of P3 . Explain. W2 = {p € P3…

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Q: Problem 8. Suppose U = {(x,x, y, y) € Fª : z, y € F}. Find a subspace W of F such that F = U e W.…

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Q: Problem 65 Let Z be a subspace of a normed space X, and y E X. Let d = d(y, Z). Prove that there…

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Q: Question 2. Are the following subsets of vector spaces subspaces? Give proofs of your answers by…

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Q: Question 1. Let U be a subspace of R5 of dimension 2. What is the value of dim U-? 3 Other

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Q: Problem 3.23. Let X = { | n e Z+}U{0} c R. (1) What is the relationship between the subspace…

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Q: Question: 4) Which of the following is a subspace of R^3? Justify your answer. i)…

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Q: Question (3): Find the basis and dimension of the subspace W: 2c a - b b- 3c:a, b,c ERER*. a) W = La…

A: We have two subspaces and we need to find the basis and dimension. This can be done as follows:

Q: QUESTION 1 Show that W = {(a,0, b) a, b = R} is a subspace of R³.

A: Result : R3 is a vector space over the field R . Theorem : A non empty subset of a vector space V…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.