show that the integraloperatort (Tx) (+)= Skctsasx Luldewin Linear and maps c[ol] +o s [osl] and XEC[@17 is normedspace

Q: (a) {(a, b, c) ER³ | 2a = 3c}. (b) {(a, b, c) ER3 | a = 0, b = 3c}. (c) {(a+b, ab, 2a + b) | a, b R}…

A: (a), (b) , (c), (d)  are subspaces .

Q: Give an example of 3 vector spaces that are not Rn. Explicitly state the definition of additon and…

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Q: If (x1,y1) + (x2,y2) = (x1x2,y1y2) and  c(x1,y1)= (cx1,cy1) are vector spaces, verify if both…

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Q: For the given matrix A What is the rref of A. What is the rref of AT A = [1 2 1 1 -1 21 0302 5 1 4 5…

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Q: Consider the following maps of polynomials S:P →P and T:P→P defined by S(g(x)) = 4 g (5) – g'(-2)and…

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Q: Suppose A is a 2x2 invertible Martix. Is the following statement true or false?  For each vector b,…

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Q: let Then Show thato- Prelurt Space IR? an Inneo on

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Q: The shape's vector set is a subspace of R3

A: solution :-

Q: Prove that the set of mxn upper triangular matrices is a subspace of Mmxn(F).

A: We have to prove that -

Q: Find oxthogonal uncdary diagonalizing an or matri'y to lMowing tor One 2 (a) (b) 3 -2 -2

A: A square matrix A is called as orthogonal matrix if AxAT=ATxA=I where AT transpose of matrix A. and…

Q: Show that ℓ^1 is a normed linear space.

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Q: ^2

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Q: Find the norm of (-4,- 1/4,3, 1/3) belong to R^4 w.r.t the Euclidean Inner Product on R^4.

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Q: Determine whether or not T = (6,-3) belongs to the null space of A' if A 1

A: the answer is

Q: Show that  ℝ2 = span([1 1], [1 -1])

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Q: Show that in 3D space, (a) k EijkEpqk = δip&jq – διαδjp

A: Note:  Since you have posted multiple questions, we will solve first question for you. Kindly repost…

Q: Verify that lxl:|Ž Ž1% P) is normed spase: and show that nokmed Spase Spase:

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Q: Show that the set of all pairs of real numbers (x, y) with the operations (X1, Y1) + (x2, Y2) = (x1…

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Q: V {(x1 , X2, X3 ) E R³ |x2 + x3 = 3} %3D nin R3'ün bir alt uzayı olup olmadığını gösteriniz.

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Q: Given the Euclidean inner product space (R³(R),+,,*), where for each x=(x1,x2,X3), y=(yı,y2,y3) ER³,…

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Q: If p4 is a vector space formed by polynomials of degree less than 3 And  s = { ax^3 + bx^2 +cx + d…

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Q: Which of the following subsets is not a vector subspace in the vector space R^3?

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Q: Give example on the inner product and same time is normed space

A: To find an example on the inner product and normed space. Definitions: Inner product space: Let V be…

Q: If on V = R² define the usual scalar multiplication « (x, y) = (« x,x y) , and addition (x1, Y1) +…

A: Concept: Vector space: Vector space is defined by the associative and commutative laws of vector…

Q: Let F: Rn -> Rn be a linear map which is invertible. Show that if A is the matrix associated with F,…

A: Given - Let F : ℝn → ℝn be a linear map which is invertible. To show - Show that if A is the inverse…

Q: A: (x, y, z) (0,0). A: (x, y, z) (xy, yz). 4: (x, y, z) (2z-x+y, x + y + z)- A: (x,y,z) (z, x). A:…

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Q: 4. A = [! -6 4 07 020 %]

A: Nul( A) i.e null space of A

Q: Show this subspace is a null space.

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Q: Find a basis for the two-dimensional subspace of R4 defined by Explain your reasoning. V := x= x1 2…

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