Use the inner product 〈 u , v 〉 = 2 u 1 v 1 + u 2 v 2 in R 2 and Gram-Schmidt orthonormalization process to transform { ( 2 , − 1 ) , ( − 2 , 10 ) } into an orthonormal basis.
Use the inner product 〈 u , v 〉 = 2 u 1 v 1 + u 2 v 2 in R 2 and Gram-Schmidt orthonormalization process to transform { ( 2 , − 1 ) , ( − 2 , 10 ) } into an orthonormal basis.
Use the inner product
〈
u
,
v
〉
=
2
u
1
v
1
+
u
2
v
2
in
R
2
and Gram-Schmidt orthonormalization process to transform
{
(
2
,
−
1
)
,
(
−
2
,
10
)
}
into an orthonormal basis.
Orthogonalize the basis {(1, 1, 1, 1),(1, 1, −1, −1),(0, −1, 2, 1)} bythe Gram-Schimidt process. Validate the results.
Use the Gram-Schmidtorthonormalization process to find an orthonormal basis of ?2(with the dot product)from the basisthe basis{(4,−3,0),(1,2,0),(0,0,4)}.
Apply Gram - Schmidt process to construct an orthonormal for R4 with the standard inner product from the basis (V1, V2, V3) where V, = (1, 1, 1, 1), V2 = (1, 2, 0, 1), V3 = (2, 2, 4, 0).
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