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.

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: 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: Use Axioms only to prove that the the solution to the equation 2x + y + 3z = 0 is a subspace of R³.

A: The given equation .To prove that the solution to the equation is a subspace of .

Q: H = 1 -3 2 -4 Determine the dimension of the subspace H, where 7 9 -6 12 2 -1 4 2 5 - -3 7

A: We know that the dimension of the vector space is the number of linearly independent vectors in the…

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

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Q: Let U1, U2, U3 – be the following subspaces of R4 Ui={(a, b, c, d)eR*| a - b+ 2c+ d=0, a - Ob - - .…

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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: 3. This problem is about set addition and subspaces. Let di and d2 = span{di}, %3D 1 U = span{d2}.…

A: Sum of two subspace

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A: According to the given information, it is required to prove that:

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: Find the dimension of the subspace spanned by the given vectors: u₁ = (1, 3, -2,5), u₂ = (0, 1,-1,…

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Q: Determine if the given subset is a subspace of R^3

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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: {: b. E M2x3 is a subspace of M3 Jige les O

A: closure property scalar multiplication satisfied

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Q: 19. Prove that the set of all vectors in R³that satisfy the equation x₁ = 3x2, is a subspace.

A: (.)  Let set  'S'  is given by ,        S=x1,x2,x3∈ℝ3  :  x1=3x2 or   S= x1,x2,x3∈ℝ3 :  x1-3x2=0…

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: 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: Let M3,3 denote the vector space of all 3 × 3 matrices. Let L3,3 denote the set of all lower…

A:

Q: Suppose U and W are two-dimensional subspaces of R3. Show that U∩W≠{0}

A: We want to show that  U∩W≠{0}

Q: Q6: Explain whether the following sets are not subspaces of R" for the appropriate value of n. a a a…

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Q: Determine whether or not W = {[a, a?, b] | a and b are real numbers} is a subspace of R³. Justify…

A: See the detailed solution below.

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

A:

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: The given subspaces of ℝ4 are U1={a, b, c, d) ℝ4| 1b=с; a=d=0};   U2={(a, b, c, d)  ℝ4| a - b + 2c +…

Q: Q-2 Show that the set of all vectors (a-3b, a+2c +4d, b+3c-d, c-d), where a, b, c, d are real…

A: We know that ℝn is a vector space of n tuples and we represent a vector x∈ℝn in the following form:…

Q: Determine if set S is a subspace or not S = {(a,0₁0) € R² } Ⓒ @ 3 S = {(₁₁ 6₂c) | b=a+c} in R (3) S…

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Q: Explain why the subset а —b S : a + b а,b€ R -2b — За of R³ is or is not a subspace of R³.

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Q: 3. Is the set of all vectors (x, y) in R2 with the usual addition and scalar multiplication, a…

A:

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: Determine all subspaces of W.

A:

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: 10. Find the dimension of the subspace of P3 consisting of all polynomials ao + ajx + a¿x² + a3x³…

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Q: Give example of subspaces of land l?wich are not closed.

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.