Let U1, U2, U3 – be the following subspaces of R4   U1={a, b, c, d) R4| 1b=с; a=d=0};   U2={(a, b, c, d) R4| a - b + 2c + 3d=0, -a +b - 2c - 3d=0};   U3= {a, b, c, d) R4| 1a – 2b – 1c - d=0, a + 2b + 0c + 2 d=0 };   Sub-Task 1. Find a basis and the dimension of U1.  Sub-Task 2. Find a basis and the dimension of U2.  Sub-Task 3. Find a basis and the dimension of U3.  Sub-Task 4. Whether R4=U1+U2, (provide a justification). Whether R4=U1 U2, (provide a justification). Sub-Task 5. Whether R4=U1+U3, (provide a justification). Whether R4=U1 U3, (provide a justification).   Sub-Task 6. Whether R4=U2+U3, (provide a justification). Whether R4=U2 U3, (provide a justification)

Q: Determine whether the set in P_2 is linearly independent.    S={x^2 , +1, 2 - 1, 2}

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Q: Let S be the subset of R2 consisting of all vectors of the form (a, b + 3). a) Show that (5, 2),…

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Q: Let U1, U2, U3 – be the following subspaces of R4   U1={a, b, c, d) R4| 1b=с; a=d=0};   U2={(a, b,…

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Determine whether W = {a + 2x + bx²|a, b = R} is a subspace of P2.

A: Explanation of the answer is as follows

Q: Q6) Determine whether the set S spans R³. If the set doesn't span R³, give a geometric description…

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Q: Let v₁ = (2,1,0,−1), v2 = (0, 1, 2, 1), and b = (1, 8, –1, −7). Let W be the subspace or R4 spanned…

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Q: One of the following subsets of R² is not subspace. Select one: а. X1 S={ X1=2x2} b. S={ ,X1 =X2} C.…

A: We will check that which subset is not a subspace of R2

Q: A set of 4 vectors in R5 is linearly independent cannot span R5 spans a 4-dimensional subspace of…

A: Given a set of 4 vectors in ℝ5.

Q: The union of two subspaces of a vector space is not necessarily a subspace.

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Q: Let W be the set of vectors in R* of the form ГЗа + 267 —а — b 3 a + c where a, b, c represent…

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Q: Let M,xn be a set of squarenx n-matrices. Is the set Mnxn a vector space? Explain. Find 2 different…

A: We find two different basis of M_2×2

Q: Please go through each option with explanation

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Q: Wi = {(a,b,c,d) E R* : a+ b+ c = 0} ve W2 = = 0, b = 0}, Being subspaces of R^4 {(a,b,c,d) e Rª : a+…

A: For the given subspaces W1 and W2, we have to calculate…

Q: 5. Show that {(1,-1,2,-3), (1,1,2,0), (3,-1,6,-6)} and {(1,0,1,0), (0,2,0,3)} do not span the same…

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Q: Cantidad1 de aditivo 3 5 NOX 19 17 14 13 12

A: Given data: Cantidade aditivo 1 2 3 4 5 NOx 19 17 14 13 12   To obtain the least square fit…

Q: Give an example of a subset (not subspace) of R3 that has an infinite number of elements, is closed…

A: A subset W of vector space V over the scalar field K is a subspace of V if and only if following…

Q: 13 - Which one of the followings is NOT the subspace of R? ? =O W = {(a,2a): a e R} W = {(a, a + 1):…

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Q: Find a minimal spanning set for the subspace spanned by the set of vectors: S={, , , }

A: The given spanning set is S=1, 0, 0, -1, 4, 4, 0, 0. We have to find the minimal spanning set.

Q: Which one of the followings is NOT the subspace of R2 ? W = {(0,–2a): a e R} - W = {(2a, a): a e R}…

A: To find which one is not a subspace.

Q: (14) Find the dimension of the subspace H = a + 4b+c+2d a + 2b + d a +5b+c+3d b+d = ahader } : a, b,…

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Q: Let W denote the subspace of R5 consisting of all vectors having coor- dinates that sum to zero. The…

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Q: a + 3b + 4d C+ d 14) Let H = :a, b, c, d in R -3a - 9b + 4c - 8d -C - d Find the dimension of the…

A: image is attached with detailed explnation

Q: {l: ol E M2x3: a = b = c = -3d } be a subspace of M2x3- Let W = d Then dimension of W is Оз 1 О4 O 2…

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Q: Determine whether each of the following sets are subspaces of R³ with the standard operations. sure…

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Q: Find a linearly independent set of vectors that spans the same subspace of R* as that spanned by the…

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Q: A base of the subspace W={ (a, b, c); a-2b+c=0} is:

A: According to the question,

Q: Suppose C is a linear code (i.e. subspace), and u,v are in the same coset of C. Show u+C = v+C

A: Definition A subset C⊆V(n,q) is a linear code if1) u + v ∈ C for all u, v ∈ C2) au ∈ C for all u ∈…

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: s = E D -16 Determine whether S spans the subspace of all 2 × 2 diagonal matioes,

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Q: et aj = (1,3, –2), a2 = (5,1, 4), and b = (6, –9,3). a) Project b onto the line through aj. b)…

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Q: 8. Let W denote the subspace of R5 consisting of all the vectors having coordinates that sum to…

A: Consider the provided question,Write the given vectors into a matrix as below,

Q: True or False, S is a subspace of R 3 x1 (8] x2 x3 S = O True O False 2x1 + x3 = 0, x1 + x2 = x3 = 0…

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Q: 8. Let W denote the subspace of R consisting of all the vectors having coordinates that sum to zero.…

A: Consider the provided question, Write the given vectors into a matrix as below,

Q: Let U1, U2, U3 – be the following subspaces of R4   U1={a, b, c, d) R4| 1b=с; a=d=0};   U2={(a, b,…

A: As per bartleby guidelines for a question only first three sub questions has to be answered please…

Q: Let U₁, U2, U3 – be the following subspaces of Rª U₁={a, b, c, d)=R4| ²b=c; a=d=0}; U2={(a, b, c,…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Exercises 1. Show that {(1,1,0,0), (1,0, 1, 1)} and {(2,-1,3,3), (0,1,-1,-1)} subspace of R4. span…

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Q: Is the union of two subspaces of a vector space, a subspace. Justify your answer.

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Q: Find a basis for the following subspace of R°: W3D {(aj + 5а2 — 2а3, 2а1+ 6а2 — аз, Зај + 7а2) : ај,…

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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.