How to calculate this? abs((4,4,m),(6,m,3),(m+3,3,4))
1 Answer
Explanation:
Reduce to a sum of scalar multiples of
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