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

If a,b,c are real numbers and `abs[[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]]=0`,show that a=b=c

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A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. Solve the following system of linear equations using matrix method. 2x...

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  2. Solve the following system of linear equations using matrix method. x-...

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  3. If A=[[2,-3,5],[3,2,-4],[1,1,-2]]find A^(-1)Using A^(-1)solve the syst...

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  4. The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs.60.The cost of ...

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

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

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  7. Evaluate|[cosalpha cosbeta,cosalpha sinbeta,-sinalpha],[-sinbeta,cosbe...

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

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  10. 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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  11. 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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  12. Let A=[[1,-2,1],[-2,3,1],[1,1,5]] verify that (A^(-1))^(-1)=A

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

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  14. Using properties of determinants prove abs[[x,y,x+y],[y,x+y,x],[x+y,...

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

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

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  17. Given Delta=|(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3)| Prove that ...

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  18. Consider a system of linear equations which is given below, 2/x+3/y+10...

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

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  20. If x,y,z are non-zero real numbers, then the inverse of A=[[x,0,0],[0,...

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