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If a,b,c are in A.P, find value of |[...

If a,b,c are in A.P, find value of `|[2y+4,5y+7,8y+a],[3y+5,6y+8,9y+b],[4y+6,7y+9,10y+c]|`

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Applying `R_1toR_1+R_3-2R_2` to the given determinant, we obtain
.|[0,0,0],[3y+5,6y+8,9y+b],[4y+6,7y+9,10y+c]|=0` (since 2b = a+c)
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A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. If a,b,c are in A.P, find value of |[2y+4,5y+7,8y+a],[3y+5,6y+8,9y+...

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  2. Evaluate |[102,18,36],[1,3,4],[17,3,6]|

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  3. Evaluate |[1,1,1],[a,b,c],[b+c,c+a,a+b]|

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  4. prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

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  5. Using properties of determinants prove the following. abs[[b+c,a,...

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  6. Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,...

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  7. Using properties, prove that |[1,omega,omega^2],[omega,omega^2,1],[om...

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  8. Without expanding the determinant prove the following. |[a-b,b-c,c-a...

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  9. Using properties of determinants show that abs[[1+a,1,1],[1,1+b,1]...

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  10. Consider the determinant D=|[1,3,5],[2,6,10],[31,11,38]| On taking 2 ...

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  11. Consider the determinant D=|[1,3,5],[2,6,10],[31,11,38]| Evaluate De...

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  12. Consider the determinant Delta =|[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-b...

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  13. Consider the determinant Delta =|[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-b...

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  14. Consider the equation |[3x-8,3,3],[3,3x-8,3],[3,3,3x-8]|=0 OperatingC1...

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  15. Consider the equation |[3x-8,3,3],[3,3x-8,3],[3,3,3x-8]|=0 Solve the ...

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  16. Without expanding the determinant prove the following. |[x,a,x+a],[y...

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  17. Without expanding the determinant prove the following. |[2,7,65],[3,...

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  18. Without expanding the determinant prove the following. |[b+c,q+r,y+z...

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  19. Without expanding the determinant prove the following. |[1,bc,a(b+c)...

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  20. Without expanding the determinant prove the following. |[a-b,b-c,c-a...

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  21. By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],...

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