Suppose that u₁ = Consider the two statements, and decide which of them is true. Statement A: If we apply the Gram-Schmidt process to these vectors, the result will be an orthogonal basis for Span{u₁, u₂}. Neither statement is true Statement B: If we apply the Gram-Schmidt process to these vectors, but use the vectors in the order 12, U₁ instead of the order u₁, U2, the Gram-Schmidt process will output a different basis. Only statement B is true and 1₂ Both statements are true = Only statement A is true

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Suppose that u₁
1
(₁
2
1 and u₂
Consider the two statements, and decide which of them is true.
Statement A: If we apply the Gram-Schmidt process to these vectors, the result will be an
orthogonal basis for Span{u₁, U₂}.
Neither statement is true
Statement B: If we apply the Gram-Schmidt process to these vectors, but use the vectors in the
order u2, u₁ instead of the order u₁, U2, the Gram-Schmidt process will output a different basis.
Only statement B is true
-
Both statements are true
H
Only statement A is true
Transcribed Image Text:Suppose that u₁ 1 (₁ 2 1 and u₂ Consider the two statements, and decide which of them is true. Statement A: If we apply the Gram-Schmidt process to these vectors, the result will be an orthogonal basis for Span{u₁, U₂}. Neither statement is true Statement B: If we apply the Gram-Schmidt process to these vectors, but use the vectors in the order u2, u₁ instead of the order u₁, U2, the Gram-Schmidt process will output a different basis. Only statement B is true - Both statements are true H Only statement A is true
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