For which value of a is the solution set of the following system x + 5y + z = b – 5 2x – 4y – z = a +b - 3 a subspace of R3?

Q: 3. Let W = M2x2(C) with zero determinant. Show that W is not a subspace of V = M2x2(C).

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Q: 1

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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: For subspaces V & V*of R° and V±R³, consider the set Š=VUV+. Is 3=R*? (always justify your answer to…

A: No! It's not true that S=R5.See the counter-example below.

Q: For which value of t is the set V below a subspace of R3? V = {(x, y, z) | 5x + 15y = 16x + 3y + 19z…

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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: 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: at | f = a is a subspace of RI0,1] if and

A: Two step test

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: Show that W = {a + bx² € P₂|a, b = R} is a subspace of P2.

A: The solution is given as

Q: Let A be a 80 x 90 matrix (80 rows and 90 columns). Does the homogeneous 0 always has nonzero…

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

A: Subspace

Q: The set of all 3 x 3 matrices of the form 1 0 0 1 Lo o 0 0 Select one: True O False + 13x3 where a…

A: Answer: The solution is as given below:

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: ind the closest point to y in the subspace W spanned by vị and v2 2 y =| 1 |,v1 = ,V2 = |-2 2 а) b)…

A: We will use the following method.

Q: 3) Explain why S, = {(x, y) E R²:y > 0} and S1 = {(x, x²): x E R} are not subspaces of R?. %3D

A: We will solve both these parts using only basic knowledge of subspaces and vector spaces (in clear…

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

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Q: Prove that the the solution to the equation 2x – y+z= 0 is a subspace of R³.

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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: Suppose a 5x7 matrix A has four pivot columns. What is dim Nul A? Is Col A = R4? Why or why not? dim…

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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: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R3 b)show that R' =…

A: Solution of the problem as follows

Q: Show that S = {(a,0, b)"|a,b E R} forms a subspace of R³.

A: The solution are next step

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

A: Consider the given equation. x+5y+z=b-52x-4y-z=a+b-3 Since, the given have three variable and the…

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

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Q: 12. Let A be a fixed n x n matrix and let S = {B e Mnxn|AB = BA}. Is S a subspace of Mnxn?

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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: [M] Determine if y is in the subspace of R4 spanned by the columns of A, where -4 3 -5 -9 -8 7 -6 y…

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Q: Let A be a fixed 10 x 10 matrix and let H be the set of all 10 x 10 matrices N with the property…

A: Given that A is fixed 10×10 matrix and H=N  NTA=AN. To find : H is a subspace of all  10×10 matrix…

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: Let W = {(" ): a + 2c = 0 and b-d = 0} be a subspace of M22. Then dimension of W is equal to: 4 2…

A: We know that  dim W = number of elements in basis of W  If S is basis of W then i) S is linearly…

Q: (a) The set V = || ER? : x = 0 or y = 0 } is a subspace of R2. (b) If A is a 3 × 3 matrix and ủ, v…

A: a) Given statement is V=xy∈ℝ2:x=0 or y=0 is a subspace of ℝ2. Given statement is False. A subspace S…

Q: the subset H={(x,y,z)∈ℝ³∣ 2x+3y-3z=4} it can be assured: * if u ∈H, v∈H , then  u⊕v∈H * if u∈H, then…

A: Given: H={ (x, y, z)∈ℝ³ ∣  2x+3y-3z=4 } To check: H is a subspace of V=ℝ³ or not. This can be done…

Q: 10 - What is the dimension of the subspace below? w = sp {C J. C 9 C 3 a) O 2 b) O 0 1 d) O -1 e) 3.

A: According to question  We have to calculate the dimension of the subspace.

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: 6 a. Show whether or not H= {(x,y, z)| 2x – y + 3z = 0} is a subspace of R3 p. Solve the following…

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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: Let A be an mxn matrix. Prove that W = {x ER" | Ax = 0} is a subspace of R", where W is the solution…

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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: Show that the solution set to a system of equations of the form au*, + Azyš, + + a, x = 0 Inn + ar =…

A: The given system of homogeneous linear equations is equivalent to a matrix equation of the form: Ax…

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: 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 w

A: Topic:- matrix

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: We have to check

Q: Let A e Mnxn and W be the set of all solutions for the homogenous linear system AX = 0. Prove or…

A: Given, A∈Mn×n and W be the set of all solutions for the homogenous linear system AX=0. We have to…

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

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Q: The set W = : 3x - y = z - 5w = 0 %3D is a subspace of RT. What is the dimension of W Select one: а.…

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