11) Is the set W = {f(x) E P(F): f(x) = 0 or f(x)has a degree n} a subspace of P(F) if n > 1? Justify your answer

Q: 5. Show that if H and H2 are two orthogonal subspaces of H, then Hin H2 = {0}. Does the converse…

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Q: 5 9. and define p : R² → R² by p(x) = Ax (that is, p = PA). Find Let A -1 -1 all 9-invariant…

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Q: 2. Find the closest point to y in the subspace W spanned by vị and v2. 3 1 -2 y V2 13 3

A: To find  The closest point y in the subspace W spanned by v1 and v2.

Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 -1 -1 projw (7) = %3|

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Q: -10 e subspace W of R" spanned by 6 and 3

A: In this question, concept of orthogonal projection is applied. Orthogonal Projection Matrix of…

Q: 10. Is 2 = {(x, y,z)| x=2 y & z=1} a subspace of R³?

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Q: 6. Show that the closure Ỹ of a subspace Y of a normed space X is again a vector subspace.

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Q: Is the set W={ f(x)e P(F): f(x)=0 or f(x) has degree n } a subspace of P(F) if n21? Justify your…

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Q: 10. Under the usual operations in R2, which of the following subsets is a subspace? (a) y = 2ar…

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Q: 10. Let Y = {(x,y,z)| z=-x}. (a) Is Y a subspace of R³? Justify. (b) Is Y a vector space? Justify.

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Q: Determine is Question 2 whether W = W = {(a; z { (a; 2; 6) | α; 6ER} subspace of R

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Q: Find the orthogonal projection ŷ of y: 6 onto the subspace W = Span { ui u2 Ex: 1.23 ||

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Q: 6. Let C"(R) denote the sct of all real-valued functions defined on the real line that have a…

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Q: the set B=E[f る,L 2 ), L3 10 in M22 the subspace of Mez spanned by B. Since carly independent Cyou…

A: Note: As per bartleby's  guideline for more than one question asked only first is to be answered…

Q: 6. Prove that an open interval (a, b) considered as a subspace of the real line is homeomorphic to…

A: An open interval a,b considered as a subspace of the real line is homeomorphic to the real line.

Q: 7) Suppose that U = x, y € F,, where Fis either C, R,or Q. One can show that U is a subspace of F*-…

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Q: Criticize the following argument: For any vector v, we have Ov = 0. So the first criterion for…

A: Let W be the subset of a vector space V. If W is itself a vector space under the operations of V,…

Q: 3 show that if w is a subspace of fini a dimensional vector space y and dim (W) = dim (V) W = V.

A: This is theorem in vector spaces

Q: 2 Find the orthogonal projection ŷ of y = onto the subspace 3 -2 W = Span { ui u2 Ex: 1.23 ŷ =

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Q: 4. Let S be the subspace of P₂ defined by S = span{1-x, 1+x, 5, 1-x², 2x}. Find dim (S), and show…

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Q: Suppose be R. Show that the set of continuous real-valued functions f on the intervai [0,1] such…

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Q: If y is in a subspace W, then y - ŷ is not zero. Select one: O True O False

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Q: 4. Prove or disprove that the set of unit 2 vectors of R2 is a subspace of R2under usual operations

A: solve the following

Q: 5 1 Find the orthogonal projection ŷ of the vector y onto the subspace W = Span { u = -7 3 Ex: 5 ||

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Q: Is M = {(x,y,z)|x is nonnegative} a subspace of R³? Yes or No? Justify or give/find a…

A: Given  M =  x, y, z  x is nonnegative

Q: 4. Show/prove whether the following is a subspace. 1 {x € R3:x =| 3| +s 2+t1,for s,t e R}

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Q: In C[−π, π], find the dimension of the subspace spanned by 1, cos 2x, cos2 x.

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Q: (b) Define subspace and Verify whether is subspace v = {(x,y,2):x,y,2ER² and x-2y+3z = 5}

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Q: Suppose that X = eR' : 2 + y + z = 0 and r²+y² = z² } . Determine (with justification) whether X is…

A: We have to check whether the set X is a subspace of the vector space ℝ3. We have to give a…

Q: Find the orthogonal projection ŷ of y = 6 onto the subspace 2 -3 W = Span { ui = 3 Ex: 1.23

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Q: that set of of degree subspace of P₂ Prove or disprove all Spolynomials is 43 not? Or

A: P2 is vector space of real polynomial of degree less or equal to 2. That is P2=px=a0+a1x+a2x2:…

Q: (b) Prove that if V is finite dimensional, then every subspace of V is also finite dimensional.…

A: (b)

Q: Suppose that A is a fixed 2x2 matrix. Let U = {X ∈ M22 | AX = XA} Question: Prove that U is a…

A:

Q: The set of all points in R3 satisfying x + y - z = 0 is a subspace. Note that the set of point…

A: It is known that any subspace of ℝ3 should contain an additivities identity element 0, 0, 0.

Q: Example 3. The operator Ax = d/dt x(t), defined on the subspace M of C[0, 1] consisting of all…

A: consider the operator d/dt on C[0, 1] with domain consisting of continuously differentiable…

Q: 6 Give a counter example to show that W is not subspace of R3. W=set of (x, y, z) where x + y = 1

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Q: pan(1,1 – x, 1 +x², 2x – 3) = span(2, 2 – x°, 2x² – x, x + 1). - %3D - -

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Q: 6. The projection of 12 onto the subspace of R spanned by ĝ V2 and a, 1 equals: -6 1,

A: 1. Let S be a non-trivial subspace of a vector space V and assume that v is a vector in V that does…

Q: 4. Let S be the subspace of P2 defined by S = span{1-x, 1+x, 5, 1-x², 2x}. Find dim(S), and show how…

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Q: 2 2 , find the closest point to v in the subspace W spanned by 6 and 3 Given i = 6. 1 12

A: To find  The closest point to V in the subspace spaneed by the given vectors.

Q: If y is not in a subspace W, then y-y is zero. Select one: O True O False

A:

Q: Consider the subspace Wof D, given by W = span (cos x, sin x, x cos x, x sin x). (a) Find the matrix…

A: f(x) = cos x + 2x cos x

Q: 2 Find the dimension of the subspace H of R spanned by – 12 8 ..... dim H =

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Q: If y is not in a subspace W, then y - ŷ is zeo. Select one: True False

A: If y is in subspace W, then the orthogonal projection of y onto W (y') is y itself.  And in that…

Q: 4. The set W of polynomials of the form ao + a₁x + a₂x² + a3x³ + a4x¹, where ao = a₂ and a₁ = az…

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Q: 5. Prove that for any subspace W of R": dim(W) Hint: the backward direction is obvious. For the…

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Q: Let A e Mnxn and W be the set of all solutions for the homogenous linear system AX = 0. Prove or…

A: Given, A∈Mn×n and W be the set of all solutions for the homogenous linear system AX=0. We have to…

Q: 3.) Determine whether the set of odd fuction: f (-x) = -f(x) which is a subset of C(-∞,0) is a…

A:

Q: (4) $5.11, Suppose X is a subspace of an inner-product space V. Show that X is a subpace of V.

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.