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Without expanding the determinant prove ...

Without expanding the determinant prove that:
`{:|(0,a,-b),(-a,0,-c),(b,c,0)|:}=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):}|

Without expanding the determinant prove that: {:|(0,p-q,p-r),( q-p,0, q-r),(r-p,r-q,0)|:}=0

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

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

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

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ALLEN -DETERMINANTS-All Questions
  1. Statement 1 is True: Statement 2 is True; Statement 2 is a correct e...

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  2. Without expanding the determinant prove that: {:|(0,p-q,p-r),( q-p,0, ...

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  3. Without expanding the determinant prove that: {:|(0,a,-b),(-a,0,-c),(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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