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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!
Attached Images Maths help.jpg (8.1 KB, 12 views) January 7th, 2019, 09:49 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra 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. Thanks from topsquark January 7th, 2019, 10:15 AM #3 Newbie   Joined: Jan 2019 From: UK Posts: 3 Thanks: 0 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 January 7th, 2019, 11:58 AM   #4
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Quote:
 Originally Posted by Johncena12 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.

Last edited by skipjack; January 7th, 2019 at 02:34 PM. Tags exam, matrix, quickly, solving Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post rudimt Algebra 3 November 14th, 2017 03:46 AM forcesofodin Linear Algebra 3 April 16th, 2010 12:30 PM phileas Linear Algebra 1 June 20th, 2009 04:31 PM

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