onsider the following subspaces of R3:  U=span[(1, 2, 1), (1, 3, 0)]  W=span[(1, 1, -1), (-1, -1, 1)]  Sub-Task (1). Find a homogeneous systems whose solution space is U. Sub-Task (2). Find a homogeneous systems whose solution space is W. Sub-Task (3). Find the dimension of UW.

Q: Which of the following is the dimension of the subspace b W = :a = b - c and a, b, c,d eRC R* ? (a)…

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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: Identify a basis for the following subspace: -a a-b 2b 3a W = A B D (9) 2 3 1 ( 1 ER 0-3 1 © [ ] C…

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Q: 1

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Q: From the 7 choices, select all that apply span{ |} + { 1 C -4 } span{ span{ span{ 1 O {0} 1 -1}+{0}…

A: Subspace must contains zero vector with respect to addition. Affine subspace is not consider here.…

Q: Find the least-squares line y = Bo + B1x that best fits the points (-3, -4), (-1, 1), (1,5), (3, 8)

A: Use least square method to solve it

Q: Given = 2 2 -6 3 6 1-0 and -6 36 find the closest point to in the subspace W spanned by

A: Given,        To  find the closest point to v in the subspace W spanned by

Q: Let A be an m × n matrix, B an n × r matrix, andC = AB. Show that N(B) is a subspace of N(C).

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Q: Is the set of all 2 x 2 matrices of the form a 1/ 1 b , where a and b may be any scalars, a vector…

A: The given set is a11b | a, b∈K. It is known that any subspace should contain the identity element.

Q: Find an orthogonal basis for the subspace Span (1, 1 + x, 1 + x²) ≤ P3. Justify your answer!

A: Using the Gram Schmidt orthogonalisation process:

Q: 2 3 Let vi V2 V3 2 and w = 3 2 a. Is w in {v1, V2, V3}? How many vectors are in {v1, v2, V3}? b. How…

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Q: and Consider the subspaces X = U = span{ [-1 −4 −4],[7 −11 −14]} W = span{ [-4 5 3],[5 2-3]} of V =…

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Q: 2. Let P3(R) be the vector space of all polynomials of degree 3 or less (and the zero polynomial).…

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Q: Let S={,,,} a Decide whether or not the vector b= is a member of Span(S). !f b is indeed a member of…

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Q: 1 . Determine which of the following subspaces of R³ are identical: U₁ = span[(1, 1, -1), (2,3,-1),…

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Q: 1 :) Given v = -2 -5 -0 and 2 -16 6 -9 4 -4 0 -6 4 find the closest point to v in the subspace W…

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Q: Let P₂ be the vector space of all polynomials of degree 2 or less, and let II be the subspace…

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Q: Use row reduction techniques to find the subspace of degree 3 polynomial functions f(x) = a + α₁x +…

A: We need to find the subspace of degree 3 polynomial functions f(x)=a0+a1x+a2x2+a3x3 that satisfy…

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: Let y=[1,6] and u=[5,7] write y as the sum of two orthogonal vectors , one in span {u} and one…

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Q: In linear algebra, the span, the column space, and the range of a matrix A are all the same…

A: In linear algebra, the span, the column space, and the range of a matrix A are all the same…

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

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

A: We have to show that given set are vector subspace or not

Q: Consider the subspaces U = span{[4 0 1],[4_1 −4]} W = span { [-5 3 3], [-5 3],[−5 4 −2]}

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Q: The Ax = b system is "solvable" only if b is a (a) Explain why the linear system Ax=b where A = 4 4…

A: The  system is "solvable" only if  is a _______ of .(a) Explain why the linear system  where  and…

Q: Solve the homogeneous system of linear equations. (Use the parameter r.) X1 + 3x2 - X3 = 0 X₁ + 4x₂…

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Q: Question 1) The dimension of the subspace of P3 consisting of all vectors of the form at³ +bt² + ct…

A: (1) Given: at3+bt2+ct+d, b=2a-5d, c=d+4a ∴abcd=a2a-5d4a+dd            =a1240+d0-511 Therefore the…

Q: 1 3 6. 3 Let vị U2 = 1 U3 = 1 and w = | 2 2 Is w in the subspace spanned by{v1, v2 , V3}? Why ? Yes,…

A: Given v1 = 10-2v2 = 311v3 = 612w = 321 The equation x1v1+x2v2+x3v3=w will have a solution if the…

Q: -10 2 -+-+- = -3 8 ) Given : -5 B-B and -4 6 -34 find the closest point to in the subspace W spanned…

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Q: Given that = 2 = -------- y = V3 = 3 10 and h -12]

A: As per the guideline, I am supposed to solve only first question from the given problems.

Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0, 3), (2, 1, –2), (0, – 1, 8),…

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Q: Given 7: -9 -10 0 find the closest point to in the subspace W spanned by -5 -6 -4 and 64

A: We have to find out the closest point of  in the subspace W spanned by Here noted that ,let,So…

Q: 1. a. b. x1 + x2 x1 2x1 - X2 Find the solution set of the following system of linear equations : - -…

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Q: Find a set of vectors that spans the subspace W CV of solutions to the following linear systems. 1.…

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Q: Consider the subspaces U = span{[1_5_3],[-4 3 -1]} W = span{[_4_2_-4],[-18_0−16]} 1x3. Find a matrix…

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Q: 2 Find bases and dimensions for the four subspaces associated with A and B: A = 1 2 4 and B= = 1 24…

A: We will find the bases and dimensions.

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.