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If Delta=|{:(1,x,x^(2)),(1,y,y^(2)),(1,z...

If `Delta=|{:(1,x,x^(2)),(1,y,y^(2)),(1,z,z^(2)):}|` and `Delta_(1)=|{:(1,1,1),(yz,zx,xy),(x,y,z):}|` then prove that `Delta+Delta_(1)=0`

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. True or False statements : If and B are invertible matrices such tha...

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  2. If A and B are two square matrices of the same order, then AB=BA .

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  3. If Delta=|{:(1,x,x^(2)),(1,y,y^(2)),(1,z,z^(2)):}| and Delta(1)=|{:(1,...

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  4. If A is a square matrix of order 3 and |3A| = k|A|, then write the val...

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  5. For what value of x is the matrix [(5-x,x+1),(2,4)] singular ?

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  6. Find the minor of a23 in |(2,-3,5),(6,0,4),(1,5,-7)|

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  7. Find the cofactor of a12 in |(2,-3,5),(6,0,4),(1,5,-7)|

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  8. If |(x+1,x-1),(x-3,x+2)|=|(4,-1),(1,3)| find the value of x.

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  9. Write the value of Delta = |(x+y, y +z , z +x),(z, x,y),(-3,-3,-3)|

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  10. If A is a 3xx3 matrix and |3A | = k |A|, then write the value of k.

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  11. For what value of 'k', the system of linear equations : x+y+z=2,2x+y...

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  12. Evaluate the determinants in exercises 1 to 2. |(2,4),(-5,-1)|

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  13. Evaluate the determinants in exercises 1 to 2. |(cos theta, - sin th...

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  14. Evaluate the following determinants: {:|(x^2-x+1,x-1),(x+1,x+1)|

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  15. If A =[{:(1,2),(4,2):}], then show that | 2A| = 4|A|.

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  16. If A = [[1,0,1],[0,1,2],[0,0,4]] then show that |3A| = 27|A|

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  17. Evaluate the following determinants: {:|(3,-1,-2),(0,0,-1),(3,-5,0)|

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  18. Evaluate the determinant : |[3,-4,5],[1,1,-2],[2,3,1]|

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  19. Evaluate the determinant : |[0,1,2],[-1,0,-3],[-2,3,0]|

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  20. Evaluate the determinant Delta = abs{:(2,-1,-2),(0,2,-1),(3,-5,0):}.

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