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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 expending or evaluating `Delta_1 and Delta_2` , show that `Delta_1+Delta_2=0`

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`Delta_1=|[a, b, c],[ x, y, z],[ p, q, r]|`

`Delta_2=|[q,-b, y],[-p, a,-x],[ r,-c, z]|`

`Delta_2=-|[q,-b, y],[p, -a,x],[ r,-c, z]|`

`Delta_2=|[q,b, y],[p, a,x],[ r,c, z]|`

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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
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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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  16. Using the factor theorem it is found that a+b , b+c and c+a are thr...

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

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