Determine, with justification, whether the following sets are subspaces of R4. --| I4 = 0 (a) S (b) S (c) S = 1 12 13 I4 IL 12 13 IA I 1² Y 12 ER¹ : : x1 + x₂ - 13 ER¹₁+ |₂|-|T3|-|T4|= -o}. ER¹ :1, y ER

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Q: Please go through each option with explanation

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Q: 12. Show that the set of all continuous function on the interval [-1,1] is a vector space under…

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Q: Q3 shew that W2 = subspace of R2 is a

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A: To identify the which of the given sets are not subspace.

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Q: Let-{ », :x, y, a, b e R and x - a = y – b}.Is W a subspace?

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Q: 14. Which of the following is a subspace of M2,3? Justify your answer. a C. C a) U = E M2.3 b = ac…

A: The solution is given as

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Q: True/False: If V is a subspace of R", then dim(V) + dim(V+) = n. True False

A: This is true and follows from a famous theorem in linear algebra.

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Q: Q4. Check the following set is a subspace of R3 or not U = ((x1, x2,x3)| x, = v2 x} %3D

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Q: 5 4 -1 33. The dimension of the null-space of A = 3 is 2 1 1 2 (A) 1 (B) 2 (C) 3 (D) 0 (E) 4 142 I3

A: Let us apply elementary row operations on the given matrix A to reduce it in a Row Echelon form.

Q: 6. Is the set of points {(x₁, x2 + 1) |x₁, x₂ € R} a subspace of R²? 7. Is the set of points…

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Q: [{-----} x+y+z=-7 A. B. Which of the following sets are subspaces of R³ ? C. D. Z X Z +2=0} 7x -5x…

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