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If a, b, c are positive and unequal show...

If `a, b, c` are positive and unequal show that value of the determinant `Delta=|[a, b, c],[ b, c, a],[ c, a, b]|` is negative.

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V PUBLICATION-DETERMINANT-QUESTION BANK
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  5. if A=[[1,-1,2],[0,2,-3],[3,-2,4]] B=[[-2,0,1],[9,2,-3],[6,1,-2]] ...

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

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

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

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

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

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

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

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

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

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

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

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