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January 7th, 2019, 09:29 AM   #1
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Solving this Matrix quickly in an Exam

Hi all,

Does anyone know the best way to answer this maths question quickly?

Get from the determinant 1 to the quadratic equation 2.

Preferably on a casio calculator,

Please see the attachments.

Thank you!
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January 7th, 2019, 09:49 AM   #2
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I wouldn't get to that quadratic. I'd simplify the matrix expression in (1) first which leads to a in integers only. From that I'd get a quadratic with integer coefficients. If I really needed the leading coefficient to be 15, I'd be able to make it so afterwards by multiplying by a constant factor.
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January 7th, 2019, 10:15 AM   #3
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Thanks but not too sure what you mean, I tried to find the determinant of each matrix then subtract them.... which gave me 8533333300-15000ω^4=0, Don't know how they got a quadratic out of it.

I also tried solving the brackets and then taking the determinant and found 90000ω^4-64002ω^2+8533.2=0
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January 7th, 2019, 11:58 AM   #4
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Quote:
Originally Posted by Johncena12 View Post
I tried to find the determinant of each matrix then subtract them
The determinant of the sum/difference of two matrices is not, in general, equal to the sum/difference of their determinants. You have to multiply the second matrix by the scalar $\omega^2$, and the first by the scalar $10^3$, and then subtract the second matrix from the first. The determinant of the result is what you are looking for.
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Last edited by skipjack; January 7th, 2019 at 02:34 PM.
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