{) Determine whether S is a subspace of R? and explain 2. Let S = E R? : x = y³ your answer.

Q: Determine whether W is a subspace of V.V=F,W= {f in F :f(0) = 0}

A: Here given V be a vector space of function over a field. and  W= {f in F :f(0) = 0}

Q: rove that W2 = {(a,b) E R² : a = 26²} is not a subspace of R?.

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Q: Which of the following is not a subspace of R? Select one: O A. W={X: I1 B W= {X:1= T, of I, = O…

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Q: 4) Which of the following is a subspace of R^3? Justify your answer. i) W={(x,y,z)|x+y+z=0} ii)…

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Q: 3. Let W = {(x,y,z): x? + y? = z}. Is W a subspace of V = R3? %3D

A: We need to check if W is a subspace or not.

Q: Which of the following are subspaces of R^3?  W ={(x, y, z) :x+y+z=0}

A: Given, W=x,y,z:x+y+z=0 Let, 2,-1,1∈W Let, -1∈F

Q: 3. State why W = {x = (x1, 2, X3, T4) E R' : a1 + x2 + x3 + a4 < 1} is not a subspace of R. (H.W)

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Q: /hat is the dimension of the subspace W = {A= [a¡j] € R5×2|a52 = 0}?

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Q: Determine the dimension of the subspace W of R4. W = {(2s – t, s, t, s)} where s and t are real…

A: Dimensions of the subspace of a vector space

Q: A (a) Show that W is a subspace of R³. (b) What is the dimension of W? _. Let u = " and let W be the…

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Q: 2. Determine whether W = {a + br + cr?; a, b, c € R, a · b.c= 0} is a subspace of P2.

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Q: Let u2 M = E R* : u; 2 0 for i = 1, 2, 3, 4 u = U3 U4 Is M a subspace of R*? Justify your answer.

A: Solution:-

Q: What is the dimensionality of the subspace spanned by V = \v +7w for the following v, w? a) b) d) 12

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Q: Q. 5 If V is any vector space, show that (0} and V are subspaces of V.

A: We have that V is a vector space.  Now, V is said to be a vector space over a field F along with 2…

Q: Determine whether W is a subspace of V

A: Given

Q: 14. Let V = R°and W = {(a, b, c) E Vla² + b² = c²}. Is W a subspace of V? If so,what is its…

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Q: 1. Determine whether w - {[:]•r:a-4-0} X1 E R? : : x1 – 23 = X2 is a subspace of R?.

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Q: Let S be the subspace of R2 spanned by e1 and let T be the subspace of R2 spanned by e2. Is S ∪ T a…

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Q: Q2) Let ( Maxa ,t, ) be a linear space over R and (За 0 0 B={0 b0+(0 -b 0):a, b,c €R} be a subspace…

A: We are given: B=3a000b000c+a000-b000c; a, b, c ∈R be a subspace of M3×3 To find: dim(B)

Q: Determine whether U is a subspace of R³. U = {(2r, –s²,t)lr,s, and t E R}

A: Vector Subspace Test: A non-empty subset W of a vector space V is a vector subspace of V if and only…

Q: Verify that V5 is a subspace of RS

A: Please check step 2 for solution.!

Q: 4. Show/prove whether the following is a subspace. {x € R3:x =| 3 +s 2+t| 1 ,for s,t e R} 2

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Q: 16. Let V be the set of vectors (x, y, z) E R³ such that r(y²+ z²) = 0. Is V a subspace of R³?

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Q: 2. Let W be the set of all vectors in R? whose first component is 2. Is W a subspace of R2? Justify…

A: It is not a subspace.

Q: S= {[a b c]€ R³|a = b+ 1} is a subspace of R. %3D صواب İbi

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Q: Which of the following is a subspace of p2? O a. R2 x, e R W = Зх, + 1 1. Ob. W = ER| x*2 2 0 C. ER?…

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Q: Which of the following is the dimension of the subspace W = :y = x+z and x, y, z, w e R} CR ? (a) 0…

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Q: Determine whether W is a subspace of V

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Q: W y x+ y+z = 0 is a subspace of R³. Select one: True False II

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Q: 16. Let V be the set of vectors (x,y, z) E R³ such that r(y² +z²) = 0. Is V a subspace of R³?

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Q: 4. Show/prove whether the following is a subspace. 1 {x € R3:x =| 3| +s 2+t1,for s,t e R}

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Q: Is (x > 0, y < 0) a subspace? Explain.

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Q: 6. Is the following a subspace? Show/prove which step fails. {x e R? : x1 + x2 = 3}

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Q: a a) Let W : 2a – b+ 3c – d = 0 }. Is W a subspace of V? Either prove that it d. is, or explain why…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: H 6 and let W be the set of all x in R3 such that u x = 0. (a) Show that W is a subspace of R³. (b)…

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Q: Which of the following subsets of R is a subspace? {(:) \ z + y° = 0} {(:) \ +2y = 0} {(;) \ z +2y =…

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Q: c) Determine whether W = {(a, b, c, d) E R*| ad – bc = 0} is a subspace of R*. %3D

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Q: Q3. Point a base of this subspace of R*: W = { (x,y,z,t) ||-y+z=0,t - = 0 }

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Q: Let U = a :a ERis a subspace of R? | 2a Is U a subset of R2? Is 0 E U?

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Q: Let S = { (a, b, c) ER° : b = a +c}. Show that S is a subspace of R'.

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Q: S = {[a b c] €R° |a = b+ 1} is a subspace of R'. صواب ihi

A: The given statement is false. i.e. S={ [a,b,c]∈ℝ3 | a=b+1 } is not a subspace of ℝ3 .

Q: {}]*+*s} {:x² + y? < 1} is a subset of R2. Show Question : The set H = %3D that H is not a subspace…

A: In the given question we have to show that the set H is not a subspace of . Concept: Here we use a…

Q: Let Uz?la :a,bE R and :c;d eR be two Subspaces of M, CR). Show that U eW= M, IR).

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Q: The set W consisting of all the points in R? of the form (x, x) is a straight line. Is W a subspace…

A: Given that the set W consisting of all the points in R2 of the form of (x, x) is a straight line.

Q: S= {[a b c]eR* |b = 0} is a subspace of R'. ylgn Ihi O

A: I have proved the basis definition of subspace

Q: W = {(x,y,z)eR³:x + z = 0} %3D

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Q: 2. Determine whether W is a subspace of V = C³ where W = {(0, b, c) E C3}

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Q: 49. Let A be a fixed n x n matrix and let S = {B e Mnxn | AB = BA} %3D Is S a subspace? Explain.

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.