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 = ,

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.3: The Inverse Of A Matrix
Problem 79E: Let A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A....
Question
100%
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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