Linear Algebra GivenB = v1 {(0, 1, 1, 1)}, v2 = {2, 1, –1, –1} , v3 {(1,4, –1,2)} , v4{(6,9,4, 2)}B' = wi {(0, 8,8)} , w2 = {–7,8, 1} , w3 {(-6,9, 1)}3 -2 1 0A = | 1 6 2 1 and T : R*→ ® such that matrix A is the-3 0 71transformation matrix in relation to bases B and B'Using the Gram-Schmidt orthogonalization process with the canonical intern product obtain1)Orthogonal base for R from B2)Orthogonal base for R3 from B'

In this problem we used Gram-Schmidt orthogonalization process.

Answered: Given B = v1 {(0, 1, 1, 1)}, v2 = {2,1,…

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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Linear Algebra

Given
B = v1 {(0, 1, 1, 1)}, v2 = {2, 1, –1, –1} , v3 {(1,4, –1,2)} , v4{(6,9,4, 2)}
B' = wi {(0, 8,8)} , w2 = {–7,8, 1} , w3 {(-6,9, 1)}
3 -2 1 0
A = | 1 6 2 1 and T : R*→ ® such that matrix A is the
-3 0 71
transformation matrix in relation to bases B and B'
Using the Gram-Schmidt orthogonalization process with the canonical intern product obtain
1)Orthogonal base for R from B
2)Orthogonal base for R3 from B'

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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