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If Delta1=|[a, b, c],[ x, y, z],[ p, q, ...

If `Delta_1=|[a, b, c],[ x, y, z],[ p, q, r]|` and `Delta_2=|[q,-b, y],[-p, a,-x],[ r,-c, z]|,` without expanding or evaluating `Delta_1 and Delta_2` , show that `Delta_1+Delta_2=0`

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
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  2. Let delta=|A x x^2 1 B y y^2 1 C z z^2 1|a n d1=|A B C x y z y z z xx ...

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  3. If Delta1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta2=|[q,-b, y],[-p,...

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  4. Without expanding show that: =|(cose c^2theta,cot^2theta,1),(cot^2thet...

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  5. Find the value of the determinant =|(2, 3, 4),( 5, 6, 8),( 6x,9x ,12 x...

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  6. Without expanding evaluate the determinant |[41,1,5],[79,7,9],[29,5,3]...

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  7. Show that |1a bc1b c+a1c a+b|=0

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  8. Without expanding evaluate the determinant |[(a^x+a^(-x))^2,(a^x-a^(-x...

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  9. If D1=|[1, 1, 1],[x^2,y^2,z^2],[x, y, z]| and D2=|[1, 1, 1],[yz, zx,xy...

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  10. Without expanding show that |[b^2c^2,b c, b+c],[c^2a^2,c a ,c+a ],[a^2...

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  11. Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alp...

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  12. If A+B+C=pi, then the value of |[sin(A+B+C),sin(A+C),cosC],[-sinB,0...

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  13. If Ar=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2, 2^(n+1)]|, the value of sum(...

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  14. If the determinant |[a,b,2aalpha+3b],[b,c,2balpha+3c],[2aalpha+3b,2bal...

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  15. If a , b , c are distinct, then the value of x satisfying |0x^2-a x^3-...

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  16. Using the factor theorem it is found that a+b , b+c and c+a are thr...

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  17. Let |x^2+3xx-1x+3x+1-2xx-4x-3x+4 3x|=a x^4+b x^3+c x^2+e be an identi...

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  18. If Dk=|[1,n,n],[2k,n^2+n+2,n^2+n],[2k-1,n^2,n^2+n+2]| and sum(k=1)^...

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  19. If Delta1=|(1, 1 ,1),(a, b, c ),(a^2,b^2,c^2)|,Delta2=|(1,b c, a),(1,c...

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  20. The value of the determinant |a^2a1cosn xcos(n+1)xcos(n+2)xsinn xsin(n...

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