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Without expanding the determinant, Pro...

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]|`

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V PUBLICATION-DETERMINANT-QUESTION BANK
  1. Prove that Delta=|[a+b x, c+d x, p+q x],[ a x+b, c x+d, p x+q],[ ...

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  2. Prove that |[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]| is...

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  3. Without expanding the determinant, Prove that |[a,a^2, bc],[b,b^2,ca...

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  4. Evaluate |[cos alpha cos beta, cos alpha sin beta, -sin alpha],[ -s...

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  5. If a,b,c are real numbers and abs[[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+...

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  6. Solve the equation |[x+a,x,x],[x,x+a,x],[x,x,x+a]|=0, a ne0

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  7. Prove that |[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]|=4a^2b^2c^...

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  8. If A^(-1)=[[3,-1,1],[-15,6,-5],[5,-2,2]] and B=[[1,2,-2],[-1,3,0],[0,-...

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  9. Let A=[[1,-2,1],[-2,3,1],[1,1,5]] verify that (A^(-1))^(-1)=A

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  10. Evaluate |[x, y, x+y],[ y, x+y, x],[ x+y, x, y]|

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  11. evaluate | [1,x,y],[1,x+y,y],[1,x,x+y] |

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  12. Using properties of determinants, prove that |[alpha, alpha^2, beta+g...

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  13. Using properties of determinants, prove that |[3a,-a+b,-a+c],[-b+a,3...

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  14. Using properties of determinants, prove that |[1,1+p,1+p+q],[2,3+2p,...

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  15. Using properties of determinants, prove that |[sinalpha,cosalpha,cos...

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  16. Consider a system of linear equations which is given below, 2/x+3/...

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  17. If a,b,c are in A.P., then the determinant |[x+2, x+3, x+2a],[x+3,x+...

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  18. If x, y, z are non zero real numbers, then find the inverse of matrix ...

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  19. Let A = [[1,Sintheta,1],[-Sintheta,1,Sintheta],[-1,-Sintheta,1]], wher...

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  20. If A(x1, y1), B(x2, y2) and C(x3, y3) are vertices of an equilateral t...

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