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Prove that : |{:(a+b+2c,a,b),(c,b+c+2a...

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

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Using properties of determinants, prove that following |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^3

Prove 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):}| .

Prove that |{:(b+c, c+a, a+b),(c+a, a+b,b+c),(a+b, b+c, c+a):}| =2(a+b+c)(ab+bc+ca-a^(2)-b^(2)-c^(2)).

Show that ,,a+b+2c,a,bc,b+c+2a,bc,a,c+a+2b]|=2(a+b+c)^(3)

Show that ,,a+b+2c,a,bc,b+c+2a,bc,a,c+a+2b]|=2(a+b+c)^(3)

Prove that: |(a,a+c,a-b),(b-c,b,b+a),(c+b,c-a,c)|=(a+b+c)(a^(2)+b^(2)+c^(2))

Prove that |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=- 2 (a^3+ b^3+c^3-3abc)

Prove that |{:(1,b,c),(a^(2),b^(2),c^(2)),(b+c,c+a,a+b):}|=(a-b)(b-c)(a+b+c)

Using properties of determinants Prove that |{:(a+b+c,,-c,,-b),(-c,,a+b+c,,-a),( -b,,-a,,a+b+c):}| = 2 (a+b) (b+c) (c+a)

Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Prove that : |{:(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2)):}|=4a^(2)b^(2)c^(2)

MODERN PUBLICATION-DETERMINANTS-FREQUENTLY ASKED QUESTIONS
  1. The maximum value of |(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)| is 1/...

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  2. Using properties of determinants prove that ((1,1, 1+3x),(1+3y,1,1),(...

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  3. If Delta=|{:(1,a,a^(2)),(a,a^(2),1),(a^(2),1,a):}|=-4, then find the v...

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  4. Prove that : |{:(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c):}|=2|{:(a,...

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  5. |[b^2c^2,bc,b+c] , [c^2a^2,ca,c+a] , [a^2b^2,ab,a+b]|=0

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  6. Without expanding, prove that the following determinants vanish : |{...

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  7. If f(x)|a-1 0a x a-1a x^2a x a|, using properties of determinants, fin...

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  8. Using properties of determinants , find the value of k if |{:(x,y,x+...

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  9. Prove that : |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^(...

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  10. If x,y,z are different and Delta=|{:(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)...

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  11. Prove that : |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+(1)/(a)+(1)/(...

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  12. Show that |[1,1,1],[a^2,b^2,c^2],[a^3,b^3,c^3]|=(b-c)(c-a)(a-b)(bc+ca...

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  13. Prove that |{:(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ac,bc,c^(2)+1):}|=1+a...

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  14. Prove that |y z-x^2z x-y^2x y-z^2z x-y^2x y-z^2y z-x^2x y-z^2y z-x^2z ...

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  15. Prove that |[-a^(2),ab,ac],[ba,-b^(2),bc],[ca,cb,-c^(2)]|=4a^(2)b^(2)c...

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  16. |[x+2,x+6,x-1],[x+6,x-1,x+2],[x-1,x+2,x+6]|=

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  17. Using properties of determinants, prove that : |{:((x+y)^(2),zx,xy),...

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