e: Let A = (4 1 -3 6 What is the null space of A?

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A: We satisfy the clouser and scaler multiplication and show that 0 vector is also in H so H is a…

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A:

Q: Is {x² – 2.x, x²+x, x²} linearly independent dependent? Prove your answer. or

A: Answer

Q: а. W- : x is a scalar |2x + y b. W = : x, y are scalars x + y c. W = +1 : x is a scalar

A: we have to check subspace.

Q: Please go through each option with explanation

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Q: Let S = -2 3 (a) Determine whether the set S is linearly dependent. Justify your answer. (b) Does S…

A: Linearly dependent set

Q: Let v1 =[1,4,-2] , v2 =[-2,-3,7] , b =[4,1,h] FIND all value(s) h such that b is in span{v1 , v2 }

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Q: If A²=0, prove that A cannot be invertible.

A: Given,If A²=0, prove that A cannot be invertible.

Q: a Let H = :a – 76 + 3c – d = 0}. First show that H is a subspace of M2×2. Then determine dim(H). d

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Q: the quotient space of a T0−space necessarily T0

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Q: Let V be the set of all pairs (x,y) of real numbers together with the following operations: (x1,y1)…

A: Given  be the set of all pairs  of real numbers together with the following operations:

Q: Let T: P₂ P₂ be a mapping defined by T(a + a₁x + a₂x²) = ao + a₁ (x + 1) + a₂(x + 1)². a) Determine…

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Q: Given 7 = find the closest point to in the subspace W spanned by -2 and -3 -1 30

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Q: {☛ | Aỡ ≤ Ổ} is a subspace of R”. O True O False

A:

Q: Find the dimensions of the following linear spaces. (a) RSX3 (b) P6 (c) The real linear space C

A: In general Rm×n is a vector space of dimension m×n. So, Dimension of R5×3 is 5×3 = 15 (a) 15

Q: -目日日 1 Let 2 2 for which value of k, the set is linearly independent? k

A: See the attachment

Q: Find the dimension of the vector space.P7

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Q: If A has a row or column consisting entirely of zeros, then Select one: a. det(A) = 1. b. det(A) =…

A: Given a matrix A whose every entry is 0.

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Q: If W is a subspace, then ||projwv||² + ||v – projwv||2 = ||v|?.

A: Given W is a subspace of a vector space V. Now projWv denotes the projection of vector v onto the…

Q: Let A = X = 1 −1 1 1 −1 1 1 -1 1 -1 −1 1 1 1 -1 - Find a non-zero vector x in the null space of A.

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Q: All computations must be shown. 1. Let pi(t) = 1+ t², p2(t) = t +t² and p3(t) = 1 + 2t + t² be…

A: Consider the provided question, given,p1t=1+t2p2t=t+t2and p3t=1+2t+t2

Q: The set {(x,3): x is in R)} is a subspace of R2

A: The given set is x,3: x is in R. It is known that any subspace should contain identity element.

Q: Let P be the vector space of polynomials of order less or equal to n. Let sub-space of P such that…

A: This is a question of vector space.

Q: Let T={[a, ) : a€R}, then T is not Borel algebra.

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Q: 2 31-1 What is the dimension of the null space Nul(A) of A = |0 0 4 0? 0 0 0 0

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Q: Is the set {(-3,0,3),(1,-1,2)(4,-2,2), (2,1,3)} of R' linear dependent over R?

A: Clearly dimension of R3 is equal to 3. So at max. we can have 3 independent sets. But here there are…

Q: State and prove the : The characteristic polynomial of any diagonalizable linear operator T splits.

A: We have to prove that: The characteristic polynomial of any diagonalizable linear operator T splits.

Q: D: Remind that the set F of all functions from R to R is a vector space. 2. Prove that for any…

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Q: [1030] Let A = 0 120 %3D V be the null space of A, and W= V.What is the dimension of W? 0 0 00 1 3.…

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Q: 4 -1 4 33. The dimension of the null-space of A = 3 2 is 2 1 1 1 2 3 (A) 1 (B) 2 (C) 3 (D) 0 (E) 4…

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Q: Let X be a pre-Hilbert space then [(x, y)|

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