1. Provide any set S1 and S2 such that: (a) Si and S2 are subspaces of R", and that (b) Si U S2 is also a subspace of R". Provide all the necessary justifications for your answer.

Q: 3. Show that the set W = {(x, 0) : x e R} is a subspace of R?.

A: In order to show W is a subspace of R2 , we need to prove W is closed under addition. For any two…

Q: 1. Parmi les sous-ensembles suivants, lesquels sont des sous-espaces vectoriels de R? U = {(r, y, z)…

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Q: Determine if the set W of vectors (x1 , x2) in R such that xr? + x2 = 1 is a subspace of R’.

A: W is not a subspace of R²

Q: 6. Let Vi and V2 be subspaces of R" such that Vi C V2. Show that any vector v E R" can be uniquely…

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Q: 3. Determine whether X1 W E R? : x² + x2 = | X2 is a subspace of R².

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Q: If v1 and v2 are in R" and H=Gen{v1, v2}, then H is a subspace of R" Justify

A: Given that : and are in  Let Now, we  have to recall  the definition of subspace of a…

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

A: Linearly dependent set

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: If S is a subspace of R", then so is the orthogonal complement of S.

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Q: (a) F = Q, V = R², and W = Z². (b) F = R, V = R², and W = {(x, y) E R? : ry > 0}. (c) F = R, V = R³,…

A: Let W≠0 be a subset of a vector space V over F with the same addition and scalar multiplication as…

Q: 3. Suppose that u and vare nonzero vectors and that S is a subspace. Prove that if u ES and v E St,…

A: Let u and v be non-zero vectors and S be a subspace. Assume that u∈S and v∈S⊥. This means that…

Q: Q.1. The set of all positive real numbers with the operations x + y = xy kx = xk Is it a vector…

A: This question is related to linear algebra topic vector space.

Q: Determine if the set W of vectors (X1 , X2) in R such that x1² + x2 = 0 is a subspace of R?.

A: We have to determine whether W is a subspace of R^2 or not.

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

A: To show any subset of vector space is a subspace , prove the following condition : Set is closed…

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

A:

Q: 1. Let "W" be the set of vectors of the form below. Show that "W" is a subspace of R4. You must show…

A: To show whether W is the subspace or not.

Q: 6. Let V be a vector space and v1, v2, V3, V4 are vectors in V. Suppose that {v1, v2, V3} are linear…

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Q: 19. Prove that the set of all vectors in R³that satisfy the equation x₁ = 3x2, is a subspace.

A: (.)  Let set  'S'  is given by ,        S=x1,x2,x3∈ℝ3  :  x1=3x2 or   S= x1,x2,x3∈ℝ3 :  x1-3x2=0…

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: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

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Q: Compute u X v.

A: Here given vector as u=3-12, v=011 These vectors can be written as u=3i-j+2kv=j+k

Q: Prove that if U and V are subspaces of R" and U <V then V+<U+.

A:

Q: 3. Determine whether the set W = {(0,x2, 3, x4) : where x2 and x4 are real numbers} is a subspace of…

A: Subspace of a vector space

Q: Show how v is orthogonal to any linear combination formed by w1 and w2

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Q: 2. Determine whether each set described is a subspace or R2. Justify your answer. H (a) The set of…

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Q: Solve the following questions: Q1) Check whether the set W = {(2a + 5b, –a + b, 3a + 4b); a, b are…

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Q: 5. For which real values of à do the following vectors form a linearly independent set in R³?

A: Solution; Consider the given vectors are: v1→ = λ, -12, -12v2→ = -12, λ, -12v3→ = -12, -12, λ Since…

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

A: Subspace of the vector space

Q: Find all values of h such that y will be in the subspace of R³ spanned 3] by v1, V2, V3 if v1 =| 2|,…

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Q: Look for or create your own set W that is a subspace of R' or R.

A: We create a subspace of ℝ3.