Suppose that U = to U and it gives you vectors F = {f1, f2, . ..}. {u1, u2, u3} is a linearly independent set in R2021. Suppose that you apply Gram-Schmidt Is F guaranteed to be orthogonal? Is F guaranteed to be orthonormal? How many vectors does F contain? Is F guaranteed to be a basis of R2021?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Question 8.
Suppose that U =
to U and it gives you vectors F =
, u2, u3} is a linearly independent set in R2021. Suppose that you apply Gram-Schmidt
{f1, f2, ...}.
Is F guaranteed to be orthogonal?
Is F guaranteed to be orthonormal?
How many vectors does F contain?
Is F guaranteed to be a basis of R2021?
Transcribed Image Text:Question 8. Suppose that U = to U and it gives you vectors F = , u2, u3} is a linearly independent set in R2021. Suppose that you apply Gram-Schmidt {f1, f2, ...}. Is F guaranteed to be orthogonal? Is F guaranteed to be orthonormal? How many vectors does F contain? Is F guaranteed to be a basis of R2021?
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