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|[b+c, a,a] , [b,c+a,b] , [c,c,a+b]|=4ab...

`|[b+c, a,a] , [b,c+a,b] , [c,c,a+b]|=4abc`

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

Prove that |(b+c,a,a),(b,c+a,b),(c,c,a+b)|= 4ac

|[1, a, a^2-b c],[1,b, b^2-c a],[1,c, c^2-a b]|=

If |[b+c,c+a,a+b],[a+b,b+c,c+a],[c+a,a+b,b+c]|=k |[a,b,c],[c,a,b],[b,c,a]| then the value of k is

|(a,b,c),(b,c,a),(c,a,b)| =

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

|(a-b-c, 2a, 2a),(2b, b-c-a,2b),(2c,2c,c-a-b)| = (a + b + c)^(3) .

Suppose a, b, c, in R and abc = 1, if A = [[3a, b, c ],[b, 3c, a ],[c, a, 3b]] is such that A ^(T) A = 4 ^(1//3) I and abs(A) gt 0, the value of a^(3) + b^(3) + c^(3) is

If Delta= |[0,b-a,c-a],[a-b,0,c-b],[a-c,b-c,0]| then Delta=

If D=[[1,a,b],[1,b,c],[1,c,a]] , then [[a,b,c],[b,c,a],[1,1,1]] =

OSWAAL PUBLICATION-DETERMINANTS-TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTIONS-I)
  1. Show that |{:(1+a^(2)-b^(2),,2ab,,-2b),(2ab,,1-a^(2)+b^(2),,2a),(2...

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  2. Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

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  3. |[b+c, a,a] , [b,c+a,b] , [c,c,a+b]|=4abc

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  4. Using properties of determinants, prove that |a+x y z x a+y z x y a+z...

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  5. Using Properties of determinants, prove that {:|(x+lamda,2x,2x),(2...

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  6. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

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  7. Prove: |2y y-z-x2y2z2z z-x-y x-y-z2x2x|=(x+y+z)^3

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  8. Using Properties of determinants, prove that: {:|(x^2+1,xy,yz),(xy,y...

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

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  10. Using Properties of determinants, prove that {:|(x+y,x,x),(5x+4y,4x,...

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  11. Using Properties of determinants, prove that: {:|(b+c,c+a,a+b),(q+r,...

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  12. IF a+b+c ne 0 and {:|(a,b,c),(b,c,a),(c,a,b)|=0, then using properties...

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  13. Prove that |[1,a,a^3],[1,b,b^3],[1,c,c^3]|=(a-b)(b-c)(a+b+c)

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  14. Prove that: (i) |{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b...

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

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  16. Find the equation of the line joining A( 1,3) and B (0,0) using det...

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  17. Using properties of determinants, prove the following: |xx+y x+2y\...

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  18. Using properties of determinants, prove the following: |alphabetag...

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  19. 15. Using properties of determinants, prove the following |[a,b,c],[a-...

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  20. [[b+c,a-b,a],[c+a,b-c,b],[a+b,c-a,c]] = 3abc - a^3 - b^3 - c^3

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