1. Consider the matrixA||71.−121 02 0(a) Use the Gram-Scmidt method tofind an orthogonal basis for Col(A).(b) Use your basis from (a) to find an orthonormal basis for Col(A).

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Answered: . Consider the matrix A = 1 0 1 1 -1 1…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2 - 1) Find the eigenvalues and eigenvectors of the matrix B = -1 1 - 2 1 -1 2) Given B = {B,, B2, ß3} where Bi B2 =|0, B3 = - 3 %3D 1 i) Show that B is a basis for R³. ii) Determine an orthonormal basis of R based on B.
1 2 -1 1 (VI). (12') Let A = 0 2 -1 Find a basis for the row space of A and a 1 4 -2 1 basis for N(A).
answer question b using reuslts of a
5. Let 1 -1 -2 0 1 A 1 2 -1 6= 2 1 1 -2 4 -1 k (a) Find RREF of augumented matrix A : (b) Find k such that A = b is consistent. Then solve i in parametric vector form. (c) Find a basis and the dimension for Nul (A). (d) Find a basis and the dimension for Col (A). (e) Find rank (A) =?
1. Show that the vectors (1/(3√2), 1/(3√√2), -4/(3√√/2)), (2/3,2/3, 1/3), (1/√√2, -1/√√2,0) form an orthonormal basis of R³. Find the coordinates of the vector (1, 4, 3) with respect to that basis.
Could someone explain the gram schmitt process in linear algebra? One example I'm having trouble with is: Perform the Gram-Schmidt process on the following sequence of vectors (in the given order), then normalize the resulting orthogonal basis.x=[−3 −6 −6], y=[−1 4 1], z=[0 −3 3].
(2) Let 1 А — 3 5 1 4 -2 Find an explicit description of Nul(A) by listing vectors that span the null space. Find a basis of Nul(A).
I need answer for 1
please solve it as soon as possible
Consider the ordered bases B = and C {[7³ -30] [5 3 1 of lower triangular 2 x 2 matrices with zero trace. That is, V = {(a): a+d= 1=0}. a. Find the change of basis matrix from C to B. 188 [00] PBC= b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C' is [M]c = [2] [M]B -2 0] 0 {[3² 9] [248]} 0 2 -4 for the vector space V - c. Find M. M
1 3. (а) Find an orthonormal basis B {ū1, ū2, đ3} of R³ such that u and the x-component of ūz is 1/3. [1 Find the coordinate vector of 3 relative to the basis B. (b) 1

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. Consider the matrix A = 1 0 1 1 -1 1 2 0 1 2 1 0 0-2 2 0 (a) Use the Gram-Scmidt method to find an orthogonal basis for Col(A). (b) Use your basis from (a) to find an orthonormal basis for Col(A).