M={[x,y,z]} € R3 ; (y=x-3z) AND (z = 5x)}. Find out if M (R) is a subspace V3 (R). Justify your claim. Please, write a more specific procedure, so I can better understand solution steps. Thank you!

Q: Find the dimension of the subspace H of IR2 spanned by the vectors and

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Q: a 2. Is the set of vectors of the form a subspace of R? Show your proof

A: **As per our guidelines we are allowed to answer only one question at a time. Kindly please re-post…

Q: Find the closest point to y in the subspace W spanned by v, and v2. 13 1 5 - 1 y = 1 1 , V2 = 1 - 1…

A: Given y=13-112,v1=11-1-2,v2=5103. The orthogonal projection of y onto span of v1, v2 is…

Q: What is the dimension of the subspace or the space of 5 x 5 matrices (ai) sucn that a11 +...+ az5 =…

A:

Q: Find the distance of the point (1, 7, -9) in R from the subspace of vectors of the form (a, 8a, b).

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Q: Assume that you are given a set of points and you want to find the regression line for this data. In…

A: Given linear system is Xa=Y is having no solution. Suppose that X be f by g, where f>g. X is full…

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: Why are [0,1] and (0,1] which are subspaces of the real number system with the usual topology not…

A:

Q: (() 2 6. Are the two subspaces span and span (() orthogonal? Justify your answer.

A: Thanks for the question :)And your upvote will be really appreciable ;)

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: 9. Is Y = {(x,y, z) | y=z} R?? a subspace of

A: ψ={(x,y,z)| y=z}

Q: 10. Under the usual operations in R2, which of the following subsets is a subspace? (a) y = 2ar…

A:

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: to the subspace W = Span{u1, u2} where 0. Find the distance from the vector y and u2 = -2 O 2 01

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

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Q: Why isn't R2 a subspace of R³?

A: For being a subspace a space must be a subset of the other. But here R2 is not a subset of R3. So…

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 dimension of the subspace spanned by the given vectors.

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Q: Verify that V5 is a subspace of RS

A: Please check step 2 for solution.!

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

A: Given that, -3x+2y+5z=0

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: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions

Q: Line with equation 2x 3y= 6 is a subspace of R2. O True False

A: False

Q: Is M = {(x,y,z)|x is nonnegative} a subspace of R³? Yes or No? Justify or give/find a…

A: Given  M =  x, y, z  x is nonnegative

Q: Find the dimension of the subspace of all vectors in R° whose second and fourth entries are equal.…

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Q: (b) Define subspace and Verify whether is subspace v = {(x,y,2):x,y,2ER² and x-2y+3z = 5}

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Q: projw(x) is not orthogonal to every vector in the subspace W. O True False

A: We have to check whether the given statement, "projwx is not orthogonal to every vector in the…

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

A:

Q: Consider the set S = y ER : 3x – 5y = 0, x + z =- . Is this a subspace of R ? Explain why or why…

A: Given set is S=xyz∈R3:3x−5y=0, x+z=4. We have to check whether the set S is the subspace of R3 or…

Q: Find the family of orthogonal trajectories of the system of circles which pass through the origin…

A: To find  The family of orthogonal trajectories of the system of circles which passes through the…

Q: Is the set of noninvertible 2 × 2 matrices a subspace of R2×2 ?

A: Given, ℝ2×2=abcd: a,b,c,d∈ℝ Let M be the set of all 2×2 noninvertible matrices  i.e.…

Q: -2 , find the closest point to v in the subspace W spanned by -2 Given v =

A: Introduction: Th formula for the projection of vector w on v is given by,…

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: The set of all points in R3 satisfying x + y - z = 0 is a subspace. Note that the set of point…

A: It is known that any subspace of ℝ3 should contain an additivities identity element 0, 0, 0.

Q: pan(1,1 – x, 1 +x², 2x – 3) = span(2, 2 – x°, 2x² – x, x + 1). - %3D - -

A:

Q: 2 2 , find the closest point to v in the subspace W spanned by 6 and 3 Given i = 6. 1 12

A: To find  The closest point to V in the subspace spaneed by the given vectors.

Q: Is Y = (x,y,z) | y=z} a subspace of R?

A:

Q: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213

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: and uz = Find the closest point to y = in the subspace W spanned by u1 = The closest point is

A:

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

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Q: Consider the regression model Y; = B1X11 + B2X2¡ + uj for i = 1,..., n. %3D • Specify the least…

A: Given- Consider the following regression model Y₁ =B₁X₁₁ + B₂X21+U₂ for i=1,2,...,n Consider the…

Q: 4. Find the distance from the vector j = to the subspace on R³ spanned by { 19: | }

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.