Let V be a subset of R³ consisting of all solutions to the linear system x-y-5z=0. Show that V is a subspace of R³. (b) Find a basis for Vand show that the basis you found is linearly independent. (a)

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A: on solving this we will get

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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

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Q: 2. Find a basis and the dimension of the subspace W = {(0,a+b,a-b); a,be R}

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Q: Let W be the subspace of P3 spanned by {t³ +t² – 2t + 1, t² + 1, t³ – 2t, 2t³ + 3t² – 4t + 3}. Find…

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Q: 5. (а) Show that the formula ((: :) (; 3)) = xã + 2yỹ+ zž + 2wũ gives M2x2(R) the structure of an…

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A: We will solve a system not equations to find the B-coordinate vector. The detailed solution is as…

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Q: Let W be the subspace spanned by the given vectors. Find a basis for W-. 1 -1 1 W1 W2 -5 -2 1

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Q: Find a basis for the given subspace of R , and state its dimension for the plane 2 x - 4 y+ 5 z = 0.…

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Q: 3.8 Using the Gram-Schmidt method, turn the basis B = (b1, b2) of a two- dimensional subspace U C R…

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Q: 4. Find a basis and the dimension of the subspace W of V = M22(R) spanned by %3D -5 2 -4 A = B = C =…

A: Given:          V = M2 × 2(ℝ) spanned by A = 1-5-42 ; B = 11-15 ; C = 2-4-57 and D = 1-7-51   To…

Q: Let H span {(-11,0, –5), (–3,0, –1), (–2,0, –1)}. A basis for the subspace H C R³ is { vector

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Q: Find a basis and dimension of the subspace described as follows:{(x, y, z, w) |2x + 5y – z=0} (0-0)…

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Q: 1. Find a basis for the subspace of R4 spanned by the vectors (1,1,-4,-3), (2,0,2,-2), (2, -2,3,2)

A: Solution:-

Q: Let W be the subspace spanned by the given vectors. Find a basis for W⊥

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A: Given a subspace S.    S=span-101,341,416 Find an orthogonal basis for S by using Gram-Schmidt…

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Q: Find a basis of the subspace of R defined by the equation 6y, + 3y, – 4y, = 0 Basis:

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Q: (11) Find a basis for the orthogonal complement of the subspace of R" spanned by the vectors V1 =…

A: We have to solve given problem;

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

A: we have to find a basis for the subspace given by −3x +2y + 5z = 0.

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Q: Find a basis for the subspace and state the dimension. p– 2q 2р-5r :P,q,r e R а. -2q +2r -Зр+ 6r| 1…

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Q: 6. a. Give a basis for the orthogonal complement of the subspace V C R' given by V = {x € R* : xị…

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Q: Find a basis for the subspace W of R³ orthogonal to {(1,1,3, 4, 1), (1, 2, 1, 2, 1)}.

A: We Use Gram Schmidt Process to Find Orthogonal basis. Use Standard Inner product as <(u1, u2),…

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

A: We will find out the required solution.

Q: Find a basis for the given subspace of R°, and state its dimension for the plane 2 x - 4 y+ 5 z = 0.…

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Q: Find a basis for the given subspace of R, and state its dimension for the plane 3x- 4y+ 5z= 0. 1 V =…

A: I am attaching image so that you understand each and every step.

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Q: 6. (a) Find a basis for the subspace of R' spanned by 1 4 7 -5 7 4 w = 4 -5 (b) Using part (a),…

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Q: Please see image

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Q: Find bases for the four fundamental subspaces of the matrix A. 15 1] A = 0 2 0 N(A)-basis N(AT) =…

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Q: Let H span {(-13, –1, -3),{-9,2, –2), (-1, –5, 0)}. A basis for the subspace H C R³ is { }. vector…

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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.