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

Q: Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4

A: Use the necessary and sufficient condition for a subspace of a vector space

Q: Show that the solution set to a system of equations of the form a + a, x = 0 + an x = 0 a m, + ... +…

A:

Q: Find the intersection of the following two affine subspaces of R4. 1 1 0 1 1 1 1 1 0 0 1 y 1 1

A: Let's find.

Q: Let AX = B be a nonhomogencous system of linear equations in n unknowns; that is, B+ 0. Show that…

A: Let us denote the solution space by W So, W = { X in Kn : AX = B } which is a subset of Kn

Q: Let W = {a + bx + cx² + dx³| a + b = 0,c – a = 0, and d – 3a = 0 } be a subspace of P3. Then the…

A: dimW = 1

Q: (c) Find a subspace U such that R³ = W₁ OU.

A: C. Hint: Use the result of part (b) in the part (c) and obtain the required result.

Q: Is W = {(x, y, z, w) | 4z – 2y = 3w – x & y+ z = -2x} a subspace? Justify your answer. If it's a…

A: Given W=x,y,z,w:4z-2y=3w-x & y+z=-2x

Q: Find the closest point to y in the subspace W spanned by v1 and v2 1 ,V2 = 1 y = V1 = -3. I • E 2 b)…

A: Here we have to find the closest point to y in the subspace W spanned by v1 and v2 .

Q: Find the closest point to y in the subspace W spanned by V1 and v2 4 y = V1= V2 = 2 -2 1 a. b. d.

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Q: a. . Is the set of vectors of the form a subspace of R³? Show your proof. La+2b

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Q: Find the closest point to y in the subspace W spanned by u, and uz. 17 1 2 %3D u1 = 0 |, u2 = - 1 2…

A: To find The closest point to y in the subspace w spanned by u1 and u2

Q: The vector x is in a subspace H with a basis B= {b, ,b2}. Find the B-coordinate vector of x. x= [x]B

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Q: Show that S = {(x, Y, z)|4x – y + 5z = 0, x, y, z E R} is a subspace of R³.

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Q: R? Which vector stretches the x + y = 0 subspace of ? Why is that? a. (2,1) b. (0,0) c.(1, -1)…

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Q: Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 17, U₁ 2, U₂ = 0-16 16 24 31…

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Q: b) Let W = { 0) * x, y e R}. Show that W is not a subspaces of M2x2. %3D

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Q: What is the dimension of the subspace W = {A = [aij] € R4x5|a45 = 0} dimW = Ex: 5

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Q: S= {[a b c]e R³|b= 3a and c = a +3} is a subspace of R' %3D ylgn O ihi O

A: To check whether S=a b c∈ℝ3|b=3a and c=a+3 is a subspace of ℝ3

Q: Which of the following sets is NOT a subspace of R'? {E} [1 Го 2 31 The set of solutions to the…

A: Following sets are given

Q: Is T = {(x,y,z)| x+2 y+3z=0} a subspace of R?

A: Subspace

Q: Find the dimension of the subspace of all vectors in R'whose second and third entries are equal. O…

A: Dimension of subspace is 6. Since dimension of R^7 is 7 and the given subspace has second and third…

Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

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Q: 5For which value of a is the solution set of the following system x + 5y +z b-5 2x - 4y - z = a+b-3…

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Q: S= {[a b c]e R°|c = ab} is a subspace of R³. صواب İhi

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Q: Find the dimension of the subspace of all vectors in R3 whose first and third entries are equal.

A:

Q: Consider the subspace S = {(7a5b)|a,b € R} Then the dimension of S corresponds to?

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Q: Is W = ((x,y) | xy=0} a subspace of R??

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Q: 9. Find the vector closest to y from the subspace of Rª spanned by Vị and v2. 3 1 Vị = 1 , y = V2 =…

A: To find  The vector closest to you from the subspace of R^4 spanned by v1 and v2.

Q: What is the value of a if the solution set of the equation x y z 1 1 2 3 1 det 2 3 4 1 O is a…

A: Given solution of the equation…

Q: In C[−π, π], find the dimension of the subspace spanned by 1, cos 2x, cos2 x.

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Q: Find a basis for the subspace given by the plane −3x + 2y + 5z = 0.

A: we have to find a basis for the subspace given by −3x +2y + 5z = 0.

Q: snip

A: We can represent the given set again as: W=xyz:x=3y+1 and z=-2y Let  w1=x1y1z1∈WThen,x1=3y1+1 and…

Q: S = {[a _b c] e R*|c = ab} is a subspace of R³. صواب İhi

A:

Q: For which value of a is the solution set of the following system х+5у +z —D b — 5 2х — 4y — z —а+b-3…

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Q: Find the closest point to y in the subspace W spanned by u₁ and ₂. 13 y = 19, U₁ = 28 O 26 20 0-2…

A: Given y=131928, u1=22-1,  u2=-134   To Find: The closest vector to y in the subspace W spanned by u1…

Q: Find the closest point to y in the subspace W spanned by u, and u2. 7 2 y = 21 u1 2 , u2* 3 38 - 1 4…

A: Given that     y = (7,21,38) , u1 = (2,2,-1) and u2 = (-1,3,4) Here we have to find the closest…

Q: Find the distance from the point x = (1, 5, –4) of R³ to the subspace W consisting of all vectors of…

A: First we will find out the orthogonal basis for the subspace W. Then we calculate the orthogonal…

Q: Find the orthogonal projection ŷ of y = -5 onto the subspace 6. -2 W = Span { uį 4 3 u2 %3D -2 Ex:…

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Q: Is Q = {(x,y,z) | x=2y & z=1} a subspace of R?

A:

Q: Find the closest point to y in the subspace W spanned by v1 and v2 y = | 1 -3 V2 = -2 а) b) 2 c) 1…

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Q: Let W = (a + bx + cx² + dx³[ c – 3d = 0 } be a subspace of Py. Then the dimension of W is equal to

A: Here we will find out dimension of W.

Q: x + 5y + z = b − 5 2x − 4y − z = a + b − 3  What value does 'a' have to take for solution space of…

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Q: What is the dimension of the subspace 0 2 3 1 H = x1 x2 x3 X4 ER¹ : 2x1 3x2 + 4x3 5x4 = 0 ?

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Q: :) Find the subspace of values that balances the chemical equation in which glucose ferments to form…

A: Solution -  We have given equation in which glucose ferments to form alcohol and carbon dioxide.

Q: Consider the system of equations on R2 y – 4a3. . Find stable and unstable subspaces.

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Q: W x + y+z = 0 }is a subspace of R³. y

A: A set S is said to a subspace of a vector space V iff for any vectors a,b∈S and for any scalars c,d…

Q: Find the closest point to y in the subspace W spanned by v1 and v2 2 1 y = -2 -3] 1 2 а) b) 2 c) 1…

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Q: Explain why S = {(r,y) : x, y € R, x > 0} is not a subspace of R²

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Q: Find the dimension of the subspace spanned by the given vectors. - 2 11 8 1 4 - 3 3 - 5 - 29 21

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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.

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