How to Use Eigenvalues of the Matrix to Identify the Sign of Definiteness - Search Videos

Use eigenvalues (characteristic roots, latent roots) to determine sign definiteness for 𝐀=[ 10 3 3 4] To find the characteristic roots of 𝐀, the determinant of the characteristic matrix 𝐀-c 𝐈 must equal zero. Thus, |𝐀-c 𝐈|=| 10-c 3 3 4-c|=0 40 c^2-14 c-9=0 c^2-14 c 31=0 Using the quadratic formula, c=(14 ±√(196-4(31)))/(2)=(14 ±8.485)/(2) c1=11.2425 c2=2.7575 With both characteristic roots positive, 𝐀 is positive definite. | Numerade

Use eigenvalues (characteristic roots, latent roots) to determine sign definiteness for 𝐀=[ 10 3 3 4] To find the characteristic roots of 𝐀, the determinant of the characteristic

Use eigenvalues (characteristic roots, latent roots) to determine sign definiteness for 𝐀=[ 10 3 3 4] To find the characteristic roots of 𝐀, the determinant of the characteristic matrix 𝐀-c 𝐈 must equal zero. Thus, |𝐀-c 𝐈|=| 10-c 3 3 4-c|=0 40 c^2-14 c-9=0 c^2-14 c 31=0 Using the quadratic formula, c=(14 ±√(196-4(31)))/(2 ...

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