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January 7th, 2019, 10:29 AM  #1 
Newbie Joined: Jan 2019 From: UK Posts: 3 Thanks: 0  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! 
January 7th, 2019, 10:49 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,561 Thanks: 2562 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.

January 7th, 2019, 11:15 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 853333330015000ω^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^464002ω^2+8533.2=0 
January 7th, 2019, 12:58 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,561 Thanks: 2562 Math Focus: Mainly analysis and algebra  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 03:34 PM. 

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