9. Which of the following subsets of M₂(R) forms a subspace? b ∞ {{ $||×+4=1} (a) a +d (c) {(% 1.)|a,b,c ER} -a b 00 {(7 ||***CH} (b) a, b, de R 1 d a (d) ~ )|a = R}

Q: Let T be the linear operator on R defined by T(x,,x, x) = (2x1, x, - x, 5x, + 4x, + x,). Then 7 is…

A: First express the linear operator in matrix form and then use the matrix to calculate the inverse…

Q: How do you know that for all a, b, c, d: ax + bx will be orthogonal to cx? + d ?

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Q: 2(a) A relation R is defined on the set A={1,2,3,4} from A to A, where R' = {(1,2); (1,3); (1,4);…

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Q: 3. Let W = M2x2(C) with zero determinant. Show that W is not a subspace of V = M2x2(C).

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Q: 2. Let S be the subspace of R5 spanned by x = (1, , (a) Find a basis for S- (b) Give a geometrical…

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Q: 1 -1 A =| 1 1 nullspace(A) = {x €R' | Ax = 0}. 1 1 (i) Show that nullspace(A) is a subspace of R'. 3…

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Q: The linear map A:R^4->R2[t] is defined by A(x,y,z,u)->(x-z)t. Then the dimension of the kernel…

A: We need to find the dimension of the kernel of the given map, A:R4→R2​[t] defined by…

Q: (a) Prove the set (A(*)./a(*),fa(a)) is linearly independent. (b) Use Gram-Schmit process to find an…

A: Given,     f1(x)=3,  f2(x)=1-x, and f3(x)=x2+2x-1

Q: One of the following is a subspace of R³. Which one? The set of points (x, y, z) in R3 such that (a)…

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Q: 4. Let W be the subspace of R³ spanned by w the orthogonal projection of 8- onto W. - (2/3) 1/3 and…

A: orthonormal vectors:- A set of non zero vectors v1, v2, v3,......, vn is called orthonormal if…

Q: Let W be the subspace of R4 spanned by S V₂ = (1, 1, 1, −1), Let V₁ =(2, 1, 2, 1), W₁ = (1, 1, 0,…

A: (a) S={v1=(2,1,2,1) , v2=(1,1,1,−1) , v3=(5,3,5,1) , v4=(−1,−2,−1,4)}Subspace W spanned by S.A…

Q: 5A Given the inner product space of polynomials with real coefficients, degree ≤n (P₁(R),+,., ° ),…

A: The angle between the vectors in inner product space:

Q: (b) For subspaces X and Y, the sum X + Y is a direct sum (denoted X + Y) if every VEX + Y can be…

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Q: 6. Determine if {(x, y): x^2 + y^2 ≥ 8} is a subspace of R^2

A: The given set is {(x, y) | x2 + y2 ≥ 8}. We check whether the set is a subspace of R2.  Since the…

Q: Consider p(x) = 3x - 2 and q (x) = x + 7. The evaluation inner product is defined as (p, q) = p (x₁)…

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Q: Find the wronskian of f1=x4, f2=-x4, f3=x2, f4=-x2

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Q: 6. Which of the following are subspaces of R° ? (x, y, z all bclong to R) (i) W {(x, y, z): x + y +…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 14. Which of the following is a subspace of M2,3? Justify your answer. a C. C a) U = E M2.3 b = ac…

A: The solution is given as

Q: 2. Find the projection from R³ onto its subspace spanned by (1, 2, −1)ª and (1,1,2).

A: Given that We  have  to  find  the projection from   onto  its  subspace spanned  by  .Let   be…

Q: Let C2(-∞,∞)={f(x) in C(-∞,∞)|f''(x) exists for all x} be the set of differential functions. Show…

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Q: -(80) (b) 2. The subspace (a) x+y+z= By in R³ is a plane whose equation is x-2=0 (c) y x-2y+z=0 (d)…

A: Here i am using linear combination and then we saw the relation between the coordinates.

Q: True or False: The linear map T:P 3(R)->R^4 defined by Tp= (p(1).p(2).p(3).p(4)) is invertible. O…

A: Given: T: P3R→R4 defined by  Tpx=p1, p2, p3, p4T1=1,1,1,1Tx=1,2,3,4Tx2=1, 4, 9, 16Tx3=1, 8, 27, 64

Q: Describe explicitly a linear transformation from V, (R) into V, (R) which has its range the subspace…

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Q: Let V = R? and K = R. Which of the following are subspaces of V? Give reasons for your answers.…

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Q: 17. Let y₁ = x₁ + x₂ and y₂ = x² + x² + 2(x₁ + x₂ + x₁x₂). (a) Use the Jacobian to test whether…

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Q: Given the inner product space of polynomials with real coefficients, degree <n (P₁(R),+,., o),…

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Q: -8 -5 -1 6 -4 --- U₁ = -5 -6 -7 -10 1 -18 Compute the distance d from y to the subspace of R4…

A: Given: y=-8-1-5-10, u1=-56-61, u2=0-4-7-18To find: The distance, d from y to the subspace of ℝ4.

Q: X2 - X1' Let L:R3 → R³ be a linear operator such that L ×2 ) =| X3 - X2 , then Ker(L) spanned by: X3…

A: we know that Ker(L) is solution of the system L(X)=0  Reveal sold the system and find the ker(L)…

Q: 1

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Q: 2) Find the indicated norms of the following linear functionals defined on RS b) f(x1,X2, X3, X4,X5)…

A: This question is about application of functional analysis

Q: T:M2x2 + P2 Where =ax + bx + (b-a) c d

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Q: 5) For each of the following subsets of F', determine whether it is a subspace of F³ : (where Fis…

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Q: (12 Which of the following statements is FALSE? (a) Each elementary matrix is invertible. (b) Let 0…

A: We will go through all the given options and check whether it is true or false.