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OCR MEI FP1 Matrices Section B Question

Hello,

Can anybody explain part iii) of this question (June 2007)?

I got it all the answers of part i) and ii) correct, but then the mark scheme just stated a substitution of k=1 into the matrix, followed by the usual solving of simultaneous equations with the inverse of A.


FP1 matrices.jpg
Reply 1
Avatar for Wunderbarr
Wunderbarr
OP
16
Anybody? :\
Reply 2
Avatar for elliot785
elliot785
if you look at matrix A, and the simultaneous equations, you will notice that the coefficients of x, y and z match the elements of the matrix (when you sub k for 1). so:

A ( x, y, z ) = ( 1, 12, 3 )
=> (A^-1) A ( x, y, z) = (A^-1) ( 1, 12, 3 )
=> ( x, y, z ) = (A^-1) ( 1, 12, 3)

so multiply the column vector by A^-1 (inverse of A which is B when you sub for k * (1/ k-n)) and the values of the resulting column vector are your values of x, y and z
Reply 3
Avatar for Wunderbarr
Wunderbarr
OP
16
Original post by elliot785
if you look at matrix A, and the simultaneous equations, you will notice that the coefficients of x, y and z match the elements of the matrix (when you sub k for 1). so:

A ( x, y, z ) = ( 1, 12, 3 )
=> (A^-1) A ( x, y, z) = (A^-1) ( 1, 12, 3 )
=> ( x, y, z ) = (A^-1) ( 1, 12, 3)

so multiply the column vector by A^-1 (inverse of A which is B when you sub for k * (1/ k-n)) and the values of the resulting column vector are your values of x, y and z


Oh wow, thanks a lot!

Can not believe I did not see that the first time -_-'

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