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Without expanding, show that : Delta =...

Without expanding, show that :
`Delta = {:|(cosec^2theta,cot^2theta,1),(cot^2theta,cosec^2theta,-1),(42,40,2)|=0`

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Write the value of the determinant |(0,a-b,a-c), (b-a, 0, b-c),(c-a, c...

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  2. Find x if |(2x, 5),(3,x)| = |(16,5),(3,2)|

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  3. Without expanding, show that : Delta = {:|(cosec^2theta,cot^2theta,1...

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

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  5. True or False statements : If and B are invertible matrices such tha...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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