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Show that |{:(a-b,b-c,c-a),(b-c,c-a,a-b)...

Show that `|{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0`

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show that det[[a-b,b-c,c-ab-c,c-a,a-bc-a,a-b,b-c]]=0

Show that abs{:(b-c,c-a,a-b),(c-a,a-b,b-c),(a-b,b-c,c-a):}=0.

Without expanding show that : |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=2|(a,b,c),(b,c,a),(c,a,b)|

Show that A=|{:(-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c):}|=4(a+b)(b+c)(c+a)

Show that |(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b)|=8abc

Show that, |{:(" "a,b-c,c+b),(a+c," "b,c-a),(a-b,b+a," "c):}|=(a+b+c)(a^2+b^2+c^2)

Show that |[b-c,c-a, a-b],[ c-a, a-b,b-c],[ a-b,b-c,c-a]| = 0 .

Show that |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3

Show that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=2|{:(a,b,c),(b,c,a),(c,a,b):}|