Writing Explain why the result of Exercise 41 is not an orthonormal basis when you use the Euclidean inner product on R 2 . 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.
Writing Explain why the result of Exercise 41 is not an orthonormal basis when you use the Euclidean inner product on R 2 . 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.
Solution Summary: The author explains why the result of Exercise 41 is not an orthonormal basis when Euclidean inner product is used on R2.
Writing Explain why the result of Exercise 41 is not an orthonormal basis when you use the Euclidean inner product on
R
2
.
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.
V = Span
({··]})
Find an orthonormal basis of R³ that contains the vector
圓
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)}.
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