Given an arbitrary basis {x1, X2, X3} in R : 7 2 - X1 = X2 = and X3 = %3D 25 7 | and following Gram-Schmidt procedure (p.4 in particular), we can cos orthonormal basis {u1, u2, u3} in R 7 -2 0 matrix X = {x1, X2, X3} - 3 1 0. 25 -7 1 and "QR-Factorization" (decomposition) X = QR. %3D Matrix Q is just an aggregation of u-vectors: Q = {u1, u2, U3}.

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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Given an arbitrary basis {x1, X2, X3} in R:
2
-
X1 =
3
X2 =
1
and
X3 =
%3D
25
|
and following Gram-Schmidt procedure (p.4 in particular), we can cos
orthonormal basis {u1, u2, u3} in R°
7
-2 0
matrix X = {x1, X2, X3}
-3
1
0.
25 -7 1,
and "QR-Factorization" (decomposition) X = QR.
%3D
Matrix Q is just an aggregation of u-vectors: Q = {u1, U2, U3}.
Calculate matrix R following Gram-Schmidt procedure (p.4):
R =
Transcribed Image Text:Given an arbitrary basis {x1, X2, X3} in R: 2 - X1 = 3 X2 = 1 and X3 = %3D 25 | and following Gram-Schmidt procedure (p.4 in particular), we can cos orthonormal basis {u1, u2, u3} in R° 7 -2 0 matrix X = {x1, X2, X3} -3 1 0. 25 -7 1, and "QR-Factorization" (decomposition) X = QR. %3D Matrix Q is just an aggregation of u-vectors: Q = {u1, U2, U3}. Calculate matrix R following Gram-Schmidt procedure (p.4): R =
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