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Prove that: {:|(1,a, a^2-bc), (1,b,b^2-c...

Prove that: `{:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0`

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Without expanding the determinant prove that |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b)):}|=0

Using the property of determinants and without expanding prove the following |{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1):}|=1+a^2+b^2+c^2

Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) ]:} ={:[( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) ]:}

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2):}|=4a^2b^2c^2

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|=(a+b+c)^3

Evaluate Delta=|{:(1,a,bc),(1,b,ca),(1,c,ab):}|

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

ALLEN -DETERMINANTS-All Questions
  1. Without expanding the determinant prove that: {:|(0,a,-b),(-a,0,-c),(...

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  2. Prove that: |[ax,by,cz], [x^2,y^2,z^2], [1,1,1]|=|[a,b,c],[x,y,z],[yz,...

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  3. Prove that: {:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0

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  4. Prove that: {:|(a^2+2a,2a+1,1), (2a+1,a+2,1),(3,3,1)|:}=(a-1)^3 .

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  5. Using properties of determinants or otherwise evaluate {:|(18, 40, 8...

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  6. Using the property of determinants andd without expanding in following...

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  7. Using the properties of determinants, prove the following |{:(a,b-c,...

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  8. Absolute value of sum of roots of the equation {:|(x+2,2x+3,3x+4), (2x...

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  9. If a+b+c=0 and |{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0 then find the val...

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  10. Suppose three digit numbers A28 , 3B9 and 52C , where A,B and C are in...

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  11. For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)...

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  12. If Dr=|2^(r-1)2(3^(r-1))4(5^(r-1))x y z2^n-1 3^n-1 5^n-1| then p...

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  13. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

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  14. Solve the following sets of equations using Cramer's rule and remark a...

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  15. Solve the following sets of equation using Cramers rule and remark ...

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  16. Solve the following sets of equation using Cramers rule and remark ...

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  17. Solve the following sets of equation using Cramers rule and remark ...

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  18. Find those values of c for which the equations: 2x+3y=3,(c+ 2)x + (c +...

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  19. Let alpha1,alpha2a n d\ beta1,beta2 be the roots of a x^2+c=0\ a...

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  20. Prove that: {:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0

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