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8. The Gramian Let a1, a2, a3, a4 have Gramian (i.e. matrix (a; aj) of inner products) given by, 2 0 1 -1 0 1 -1 2 1 -1 1 2 0 -1 0 2 Notice that det G = 0 and thus, a₁ A a2 ^ az A a4 = 0 i.e. these four vectors are linearly dependent. Find, |a3 ^ a4. (A) √2 (B) 4 (C) 0 (D) 2 (E) 1

8. The Gramian Let a1, a2, a3, a4 have Gramian (i.e. matrix (a; aj) of inner products) given by, 2 0 1 -1 0 1 -1 2 1 -1 1 2 0 -1 0 2 Notice that det G = 0 and thus, a₁ A a2 ^ az A a4 = 0 i.e. these four vectors are linearly dependent. Find, |a3 ^ a4. (A) √2 (B) 4 (C) 0 (D) 2 (E) 1

Advanced Engineering Mathematics
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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8. The Gramian Let a1, a2, a3, a4 have Gramian (i.e. matrix (a; aj) of inner products) given by, 2 0 1 -1 0 1 -1 2 1 -1 1 2 0 -1 0 2 Notice that det G = 0 and thus, a₁ A a2 a3 a4 = 0 i.e. these four vectors are linearly dependent. Find, |a3 ^ a4. bayara (A) √2 (B) 4 (C) 0 (D) 2 (E) 1
Transcribed Image Text:8. The Gramian Let a1, a2, a3, a4 have Gramian (i.e. matrix (a; aj) of inner products) given by, 2 0 1 -1 0 1 -1 2 1 -1 1 2 0 -1 0 2 Notice that det G = 0 and thus, a₁ A a2 a3 a4 = 0 i.e. these four vectors are linearly dependent. Find, |a3 ^ a4. bayara (A) √2 (B) 4 (C) 0 (D) 2 (E) 1
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