Question

FInding the Lambda of a 3x3 matrice.

Answer 1

\[\left[\begin{matrix} \lambda-4 & 0 & 0 \\ 0 & \lambda & 2 \\ 0 & 3 & \lambda-1\end{matrix}\right]\]

find \(\lambda\) !!

Answer 2

that is a 3x3 matrix.

If you are trying to find the eigenvalues then take the determinant and set it equal to zero and solve for \(\lambda\)

Answer 3

ahh my bad, i typed wrong

Answer 4

i got
\[\lambda^3 - 5\lambda^2-2\lambda+24 = 0\]

Answer 5

\[\lambda(\lambda^2-5\lambda-2) + 24=0\]
what should i do after this?

Answer 6

find what values for lambda satisfy the equation

Answer 7

i am stucked

Answer 8

so lambda = ?, ??, ???

A third order polynomial should yield 3 roots, though they might not be distinct. Those are what your lambda values are

Answer 9

x(x^2−5x−2)+24=0

Find the roots

Answer 10

wait a minute

Answer 11

λ = -2,3,4

Those are your eigenvalues

Answer 12

\[\lambda (\lambda^2 - 5\lambda - 2 + 8 - 8) + 24 = 0 \]
\[\lambda(\lambda^2 - 5\lambda + 6 - 8) + 24 = 0\]
\[\lambda([(\lambda -2) (\lambda - 3)] - 8) + 24 = 0\]

Answer 13

\[\lambda((\lambda-2)(\lambda-3) - 8) = -24\]

Answer 14

You have to multiply everything out, and combine terms of the same power, then factor

Answer 15

i took a shortcut

http://www.wolframalpha.com/input/?i=x%28x^2%E2%88%925x%E2%88%922%29%2B24%3D0

Answer 16

ahh..,

Answer 17

i see

Answer 18

thank you !!