How to calculate this? #abs((4,4,m),(6,m,3),(m+3,3,4))#

1 Answer
George C.
Apr 28, 2017

#abs((4, 4, m), (6, m, 3), (m+3, 3, 4))=-m^3-3m^2+46m-96#

Explanation:

Reduce to a sum of scalar multiples of #2xx2# determinants and hence to the value.

#abs((color(red)(4), color(green)(4), color(blue)(m)), (color(red)(6), color(green)(m), color(blue)(3)), (color(red)(m+3), color(green)(3), color(blue)(4)))#

#=color(red)(4)abs((color(green)(m), color(blue)(3)), (color(green)(3), color(blue)(4)))+color(green)(4)abs((color(blue)(3), color(red)(6)), (color(blue)(4), color(red)(m+3)))+color(blue)(m)abs((color(red)(6), color(green)(m)), (color(red)(m+3), color(green)(3)))#

#=color(red)(4)((color(green)(m))(color(blue)(4))-(color(blue)(3))(color(green)(3)))+color(green)(4)((color(blue)(3))(color(red)(m+3))-(color(red)(6))(color(blue)(4)))+color(blue)(m)((color(red)(6))(color(green)(3))-(color(green)(m))(color(red)(m+3)))#

#=4(4m-9)+4(3m+9-24)+m(18-m^2-3m)#

#=16m-36+12m-60+18m-m^3-3m^2#

#=-m^3-3m^2+46m-96#

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