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|[a,b,c],[a-b,b-c,c-a],[b+c,c+a,a+b]|=a^...

`|[a,b,c],[a-b,b-c,c-a],[b+c,c+a,a+b]|=a^3+b^3+c^3-3abc`

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det[[a,b,ca-b,b-c,c-ab+c,c+a,a+b]]=a^(3)+b^(3)+c^(3)-3abc

Show that |[b+c,c+a,a+b] , [a+b,b+c,c+a] , [a,b,c]|=a^3+b^3+c^3-3abc

|(1,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=a^(3)+b^(3)+c^(3)-3ab

Prove the identities: det[[a-b,b-c,c-ab+c,c+a,a+b]]=a^(3)+b^(3)+c^(3)-3abcdet[[a-b,b-c,c-ab+c,c+a,a+b]]=a^(3)+b^(3)+c^(3)-3abc

if abc!=0 and if |[a,b,c],[b,c,a],[c,a,b]|=0 then (a^3+b^3+c^3)/(abc)=

15.Using properties of determinants,prove the following det[[a-b,b-c,c-ab+c,c+a,a+b]]=a^(3)+b^(3)+c^(3)-3abc,]|=

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)

If a,b,c in R such that a^3+b^3+c^3=2 and |[a,b,c],[b,c,a],[c,a,b]|=0 then find abc

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

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

CBSE COMPLEMENTARY MATERIAL-MATRICES AND DETERMINANTS-FOUR MARK QUESTIONS
  1. Find the value of k, if: |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=k...

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  2. If x,y and zinR, and Delta=|(x,x+y,x+y+z),(2x,5x+2y,7x+5y+2z),(3x,7x...

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  3. If |(1,a^2,a^4),(1,b^2,b^4),(1,c^2,c^4)|=k|(1,1,1),(a,b,c),(a^2,b^2,c^...

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  4. Evaluate the following: |[1,,a^2-bc],[1, b,b^2-ac],[1,c,c^2-ab]|

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  5. |(1,a^(2)+bc,a^(3)),(1,b^(2)+ac,b^(3)),(1,c^(2)+ab,c^(3))|=-(a-b)(b-c)...

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  6. Using properties of determinants, prove that following: |"a"+"b"+2...

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

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

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

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  10. Prove that | ((b+c)^2, a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2)|=2...

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  11. Given A=[(0,-1,2),(2,-2,0)]andB-[(0,1),(1,0),(1,1)]. Find the product ...

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  12. Using properties of determinants, solve the following for x: |x-2 ...

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  13. FInd x when |[x+a, a^2, a^3] , [x+b, b^2, b^3] , [x+c, c^2, c^3]|=0 wh...

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  14. Express the matrix [3-2-4 3-2-5-1 1 2] as the sum of a symmetric and s...

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  15. If x=-4 is a root of a Delta=|(x,2,3),(1,x,1),(3,2,x)|=0, then find th...

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  16. Using properties of determinants. Find the value of 'x' |(4-x,4+x,4+...

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  17. prove that |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(1-x),x(x-1)(x-2),x(x+1)(...

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

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  19. If A=[(2,-1,1),(-1,2,-1),(1,-1,2)] show that A^(2)-5A+4I=0 Hence fin...

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  20. It A=[(-1,2,0),(-1,1,1),(0,1,0)] show that A^(2)=A^(-1)

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