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FP2 Matrices Question watch

1. (Original post by F3rnw3h)
Are you struggling? Posting for fun?

If you're stuck on it, post your attempt.

2. I first used the equation 'Ms=λs,
and found the eigenvalue to be -1, and k to be -12,

I then used the equation det(M-λI)=0 using Sarrus' method giving me:

16(8-λ) - 30(-3-λ) - 24(-3-λ)
= 38 λ + 290 (multiplying right to left)

(-3-λ)(8-λ)(-3-λ) + 96 + 120
= -λ^3 + 2λ^2 + 39λ + 72 (multiplying left to right)

Giving the characteristic equation:

= -λ^3 + 2λ^2 + λ - 263

However, substituting λ=-1 into this equation does not give me zero :/
I'm not sure where I've gone wrong?

Thanks for any help!
3. (Original post by RDKGames)
Are you struggling? Posting for fun?

If you're stuck on it, post your attempt.
Ah sorry - accidentally pressed enter and it submitted before I wrote anything xD
I've just reposted it -
https://www.thestudentroom.co.uk/sho....php?t=5016162
4. (Original post by F3rnw3h)
I first used the equation 'Ms=λs,
and found the eigenvalue to be -1, and k to be -12,

I then used the equation det(M-λI)=0 using Sarrus' method giving me:

16(8-λ) - 30(-3-λ) - 24(-3-λ)
= 38 λ + 290 (multiplying right to left)

(-3-λ)(8-λ)(-3-λ) + 96 + 120
= -λ^3 + 2λ^2 + λ - 263 (multiplying left to right)

However, substituting λ=-1 into this equation does not give me zero :/
I'm not sure where I've gone wrong?

Thanks for any help!
5. (Original post by RDKGames)
I've multiplied it out again and still seem to get the same characteristic equation, so not sure where I've gone wrong
6. (Original post by F3rnw3h)
I've multiplied it out again and still seem to get the same characteristic equation, so not sure where I've gone wrong
I just did it with the Rule of Sarrus and got the correct answer. Check your signs, it should be
7. (Original post by _gcx)
I just did it with the Rule of Sarrus and got the correct answer. Check your signs, it should be
Thanks! But I left them as positives and then subtracted that from my multiplication left to right, so it should give the same answer

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