A question on algebra Problem 3. (a) Find a basis of a subspace U in R given by a system:S21- 2+2r3+z, = 0- 12 + 3r3 + 2z, =0(b) Extend the basis constructed in (a) by adding one more vector to geta basis of the subspace W, which is a solution space for r-T2+2r3+4 = 0.

Name: A question on algebra Problem 3. (a) Find a basis of a subspace U in R
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: A question on algebra Problem 3. (a) Find a basis of a subspace U in R given by a system:S21- 2+2r3+z, = 0- 12 + 3r3 + 2z, =0(b) Extend the basis constructed in (a) by adding one more vector to geta basis of the subspace W, which is a solution space

3) a)The subspace U of ℝ4 is given by the system x1-x2+2x3+x4=0 x1-x2+3x3+2x4=0

Math

Advanced Math

Problem 3. (a) Find a basis of a subspace U in R' given by a system: T1- 2 + 2.r3+r1 1-12+3r3 + 2x, = 0 (b) Extend the basis constructed in (a) by adding one more vector to get basis of the subspace W, which is a solution space for r,-r2+2r3+1 =0.

Problem 3. (a) Find a basis of a subspace U in R' given by a system: T1- 2 + 2.r3+r1 1-12+3r3 + 2x, = 0 (b) Extend the basis constructed in (a) by adding one more vector to get basis of the subspace W, which is a solution space for r,-r2+2r3+1 =0.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...

See similar textbooks

Similar questions

Solve: (a) If a 7 x 9 matrix A has rank 5, what are the dimensions of the fourfundamental subspaces of A? (b) If a 3 x 4 matrix A has rank 3, what are the dimensions of R(A) and N(AT)?
Based on other problems I believe the dimension is 3, but I'm not sure how to find a basis given this subspace.
Find the coordinate matrix of x = (−2, 1, 3) in R3 relative to the standard basis S = {(1, 0, 0), (0, 1, 0), (0, 0, 1)}.
Find the coordinate matrix ofp = 4 − 2x2 + 3x3relative to the standard basis for P3,S = {1, x, x2, x3}.
1. 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 subspace of all 2 x 2 matrices?
The sets B={[1 2 2 1]T; [1 0 2 0]T; [2 0 4 -3]T} and B'={[0 2 0 1]T; [2 1 4 -1]T; [1 2 2n 4]T} are bases for the same subspace of R4. Find the matrix M that translates B' coordinates to B coordinates.
I have a question regarding Linear Algebra chapter 5.3: If I am trying to determine if a matrix A= [ 0 1 1 2 1 2 3 3 2 ] is diagonizable, and the solution I got for the third row was 1 = 0, does this mean that the matrix is not diagonizable since the eigenvalue = 0 proves that the matrix is inconsistent? Or am I able to still get the basis vector for the eigenspace?
1. Consider the system of linear equations Ax = b below:x - y - z = 22x + 4y + 6z = 84x + 2y + 4z = 12 Is its coefficient matrix A singular and will you classify the columns of the coefficient matrix A as linearly dependent or linearly independent? Will the column vectors of the coefficient matrix A span the vector space V consisting of all vectors [x y z]T where x, y and z are real numbers? Will the column vectors in the coefficient matrix A form a basis for the vector space consisting of all vectors [x y z]T where x, y and z are real numbers.
Suppose masses m1, m2, m3, m4 are located at positions x1, x2, x3, x4 in a line and connected by springs with constants k12, k23, k34 whose natural lengths of extension are l12, l23, l34. Let f1, f2, f3, f4 denote the rightward forces on the masses, e.g., f1 = k12(x2 - x1 - l12). (a) Write the 4 x 4 matrix equation relating the column vectors f and x. Let K denote the matrix in this equation. (b) What are the dimensions of the entries of K in the physics sense (e.g., mass times tim, distance divided by mass, etc.)? (c) What are the dimensions of det(K), again in the physics sense? (d) Suppose K is given numerical values based on the unit meters, kilograms, and seconds. Now the system is rewritten with a matrix K' based on centimeters, grams, and seconds. What is the relationship of K' to K? What is the relationship of det(K') to det(K)?
Find a basis for the subspace of R3 spanned by S.S = {(4, 4, 8), (1, 1, 2), (1, 1, 1)}
The cosine space F3 contains all combinations y(x) = A cos x+ B cos 2x+C cos 3x. Find a basis for the subspace with y(O) = 0.
What conditions on the eigenvalues of an n×n matrix A would guarantee that the system x′ = Ax has at least one solution satisfying x(t) = x0 for all t, where x0 is a constant vector?