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Using the property of determinants andd ...

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

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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

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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

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

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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

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

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(2,7,65),(3,8,75),(5,9,86):}|=0

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

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ALLEN -DETERMINANTS-All Questions
  1. Prove that: {:|(a^2+2a,2a+1,1), (2a+1,a+2,1),(3,3,1)|:}=(a-1)^3 .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...

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

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  20. If u=a x^2+2b x y+c y^2,\ y^(prime)=a^('2)+2b^(prime)x y+c^(prime)y^2,...

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