Consider the set S = yl E R : 4x +6z=7y, x – 13y=0 . Is this a subspace of R ? Explain why or why not.

Q: Answer the following: A SIAII OT VOITOUG 4. Determine if the odd functions (f(-x) = -f(x)) are a…

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

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Q: State the dimension of the following subspace, The solution space {(a,b,c): a-3b+c=0, b-2c=0,…

A: We have to find the dimension of the subspace.

Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. 3 - 1 y = 0 V₁ = 1 16 1 - 4 - 1…

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Q: Find the closest point to y in the subspace W spanned by v₁ and v2. y= 3 -1 1 16 V1 11 1 -4 1 5 V2 =…

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

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Q: 5а+ 2b Decide whether the set of all vectors of the form is a subspace of R³ or a

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Q: Is R2 a subspace of the complex vector space C²? Justify your Yes/No answer.

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Q: Show that the set T= {(a, b, c, d): 2a-3b+Sc-d=0} is a subspace of R'.

A: Given T=abcd∈ℝ4:2a-3b+5c-d=0 Let A be a 1×4 matrix defined by: A=2-35-1 Then the equation…

Q: Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 19, Un 28 国 26 20 -2 -26…

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Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. y = 5 - 1 1 18 V₁ 1 - 2 - 1 3 V2…

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Q: Determine whether W = {(a,2,b)la, b ER} is a subspace of R³.

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Q: Which of the following sets are subspaces of R³: W1 = {(x1, x2, X3) : x3 = 2x1 – 4x2}; W2 = {(x1,X2,…

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

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Q: 2t 6. Let H be the set of all vectors Show that H is a subspace of R³. What is the -t dimension of…

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Q: 2. Determine which of the following is a subspace of R". (a) {(x1,x2,...X) 1 x = 0} (b) {(x1,…

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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: If v is in R°, then the set of vectors a with v x a = 0 is a subspace.

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Q: { 2) \a,b e R}. Let W = Decide whether W is a subspace of M22. Give reasons for your answer.

A: This is a question of vector space.

Q: Find a unit vector in the direction in which f(x, y, z) = 2x³z² + 2y³z + 250z − 4 increases most…

A: A function f increases most rapidly in the direction of The maximum rate of change is

Q: x - 4y = z) x + y = 0 is a subspace of R³. State any theorems that you 4. Show that the set H = use.

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Q: Determine: if W = the set of all vectors in R2 whose components are integers is a subspace.

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Q: Consider the system of equations on R² -x Y – 4x³ . 1. Find stable and unstable subspaces.

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Q: V = a C |a+b+c= 2, 3a - c = 1, a-b+c=3

A: We know that any subspace of a vector space should contain the zero vector of the vector space.

Q: Let U 2xy = 1. Note that geometrically, U is a linear. Is U a

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