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.

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

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

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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.

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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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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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