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Consider the symmetric matrix 0 3 0 M = 3 0 0 0 0 -1 Find constants C1 and C2 such that the quadratic form q(v) = vMv satisfies €₁||||² ≤ q(v) ≤ 2||||² for all VER³ with the condition that there exists two vectors u, w ± 0 such that q(u) 9(w) = c2l|w1|² = ,

Consider the symmetric matrix 0 3 0 M = 3 0 0 0 0 -1 Find constants C1 and C2 such that the quadratic form q(v) = vMv satisfies €₁||||² ≤ q(v) ≤ 2||||² for all VER³ with the condition that there exists two vectors u, w ± 0 such that q(u) 9(w) = c2l|w1|² = ,

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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Consider the symmetric matrix 0 3 0 M = 3 0 0 0 -1 Find constants c₁ and c2 such that the quadratic form q(v) = v·Mv satisfies c₁||v||² ≤ q(v) ≤ c₂||||² for all ER³ with the condition that there exists two vectors u, w ± Ổ such that q(u) q(w) = c2|lw||². = ²
Transcribed Image Text:Consider the symmetric matrix 0 3 0 M = 3 0 0 0 -1 Find constants c₁ and c2 such that the quadratic form q(v) = v·Mv satisfies c₁||v||² ≤ q(v) ≤ c₂||||² for all ER³ with the condition that there exists two vectors u, w ± Ổ such that q(u) q(w) = c2|lw||². = ²
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