Which of the following are vector spaces? Justify your answer. (a) The set of all polynomials of degree 3. (b) The set of all vectors x = (x1, x2, x3), satisfying 3x₁ + 5x29x3 = 2023. (c) The set of all vectors x = (x₁, x2, x3), satisfying 2024x₁ + X2 = (d) The set of all 3 × 3 matrices such that Ax= (e) The set of all n × n (n ¤ N) diagonal matrices. - x3 = 0. - O has a unique solution.

Q: Let v1 and v2 be vectors in an inner product space V.(a) Is it possible for |{v1, v2} | to be…

A: It is given that,  v1, v2 be the vectors in an inner product space V. a) We have to determine that…

Q: If x is an n-vector, show that x + 0 = x.

A: Given, If x is an n-vector.

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A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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Q: Use coordinate vectors to test whether the following sets of polynomials span P, Justify your…

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Q: 6. Prove that A ·B+ |A x B|< 2|A||B|| for arbitrary vectors A, B and C.

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Q: Which of the following are vector spaces? Justify your answer. (a) The set of all polynomials of…

A: Here we check the part (d) and (e) is vector space or not.

Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

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Q: Find a linear map T that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

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Q: Find a complex vector d so that if F{(fo, ƒ1, ƒ2 ƒ3)} = ċ then F{(−fo, − ƒ₁, 0, 0)} = č ® ā.

A: According to the given data, find the vector d:

Q: Describe the zero vector (the additive identity) of the vector space. P3 x + ]+² +

A: We have to describe the zero vector (the additive identity ) of the vector space P3.

Q: Q2. ()- Work out a - 2b as a column vector.

A: Given

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Q: (a + n ) ² − ( ₁ + n ) z

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Q: Under what condition for the real numbers a,b the vectors (b,-1)(2,a) are linearly related

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Q: 1. Let x = i +4j + 2k and y = i - 3j - k. In this question, write all vectors in i, j, k notation.…

A: Let (a) To find .(b) To find .(c) To find .(d) To find .

Q: Since it's an if and only if proof, don't you have to prove "if linearly dependent, then scalar…

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Q: = x + 2x + 3 is a vector in R3. Question B): The set Select one: is a linearly independent O True…

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Q: One of the following vectors lies in span{ 2+ x + x2, 3+x- 2x2} (A) 2+ 2x + 7x? (B) 2 + 2x + 5x? (C)…

A: The linear span of the given vectors is of the form a(2+x+x2)+b(3+x-2x2)