let b={(0,2,-2)(1,0,-2)} be a basis for a subspace of R^3 and let x=(-1,4,-2) be a vector in the subspace. find the coordinate matrix of x relative to B. use the GRAM-SCHMIT orthonormalization process to transform B into an orthonormal set B'. find the coordinate matrix of x relative to B'.
let b={(0,2,-2)(1,0,-2)} be a basis for a subspace of R^3 and let x=(-1,4,-2) be a vector in the subspace. find the coordinate matrix of x relative to B. use the GRAM-SCHMIT orthonormalization process to transform B into an orthonormal set B'. find the coordinate matrix of x relative to B'.
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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let b={(0,2,-2)(1,0,-2)} be a basis for a subspace of R^3 and let x=(-1,4,-2) be a vector in the subspace. find the coordinate matrix of x relative to B. use the GRAM-SCHMIT orthonormalization process to transform B into an orthonormal set B'. find the coordinate matrix of x relative to B'.
Expert Solution
Step 1
The given basis vector are .
The given vector is .
(a)
Therefore the vector can be written as:
Solving which, yields .
Hence the vector can be written as:
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