7. Let V be the vector space of polynomials in two variables x and y of degree at most two: V = {ax² + bxy + cy² + dx + ey + ƒ | a, b, c, d, e, ƒ ≤ R}. Let T be the linear operator on V defined by T(g(x, y)) = Ә 29(x, y) + g(x,y). ду Find the Jordan canonical form of T.

Q: 2. Using the definition of linear dependence prove that any set of vectors containing the zero…

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Q: Which one of the following is a subspace of the vector space M2 (R) of 2 x 2 matrices? ss (X) the…

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A: The properties of subspaces: Closed under multiplication; Closed under addition; Contains the…

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Q: What is the dimension of the vector space S=abc detEM2x3(R): a=b=c=0}

A: Dimension of vector space is number of element in basis

Q: (H) {| R uzayı 2)

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Q: let W be an inner product space and let w1 and w2 be vectors in W. suppose ll w1 ll =5^1/2 and ll w2…

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Q: Let W1=span{(1,1,0),(-1,1,0)} and W2=span{(1,0,2),(-1,0,4)} Proove W1+W2=R^3

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Q: . Consider M₂ (R) as a vector space and its subspaces U₁= {A € M₂(R): A¹ = A} and U₂ = {A € M₂(R) :…

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Q: Let Rz, be a linear space with all polynomials p(x)= ar² + bx+c(a,b,c R) whose degree is no more…

A: Note: As per our guidelines, we can answer the first question. Please repost the remaining…

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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

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A: The main objective is to check {p1,p2,p3} linear independent and basis of P2.

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Q: Show that V = W₁ © W₂ for the given vector space V and the given subspaces W₁ and W₂. (a) V = R³, W₁…

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Q: 33. Let V - P3 be the vector space of polynomials of degree <3, and let p₁(x) = (2-x)² and p₂(x) =…

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Q: II. Decide which of the following are subspaces of corresponding vector spaces: C R?

A: Vector space.

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A: Solution of the problem as follows

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A: Given :  P3 is the vector space of polynomials of degree less than or equal to 3. To prove :  We…