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By using properties of determinants, sh...

By using properties of determinants, show that : `|[1,x,x^2],[x^2,1,x],[x,x^2,1]| = (1-x^3)^2`

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By using properties of determinants, show that : |[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]| = (5x+4)(4-x)^2

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Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]| = (1+pxyz)(x-y)(y-z)(z-x)

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By using properties of determinants, show that |{:(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4):}|=(5x+4)(4-x)^(2)

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Using the properties of determinants, prove that following : |{:(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(1-x),x(x-1)(x-2),x(x+1)(x-1)):}|=6x^(2)(1-x^(2))

Using the properties of determinants, find the value of x, if: {:|(x+2,x+6,x-1),(x+6,x-1,x+2),(x-1,x+2,x+6)|=0

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. By using properties of determinants, show that : |[1,x,x^2],[x^2,1,x...

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  2. Let A be a square matrix of order 3xx3, then prove that |kA|=k|A|.

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  3. If any two rows (or columns) of a determinant are identical, the value...

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  4. Answer in one word. {:|(3,1,6),(5,2,10),(7,4,14)|

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

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  6. Write the value of the following determinant abs{:(a-b, b-c, c-a),(b-c...

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  7. Use properties of determinants ot evaluate: {:|(2,a,abc),(2,b,bca),(...

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  8. Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y)...

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

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  10. Use properties of determinants ot evaluate: {:|(2,3,1),(4,6,2),(1,3,...

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  11. Use properties of determinants ot evaluate: {:|(2,3,5),(261,592,127)...

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  12. Show that x=1 is a root of the equation: {:|(x+1,2x,-11),(2x,x+1,-4...

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  13. If p,q,r ar in A.P. write the value of : {:|(x+1,x+2,x+2p),(x+2,x+3,...

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  14. Without expanding, prove that the following determinant vanishes. |...

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  15. Without actual expansion, prove that the following determinants vanish...

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  16. Without actual expansion, prove that the following determinants vanish...

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  17. Without actual expansion, prove that the following determinants vanish...

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  18. Without actual expansion, prove that the following determinants vanish...

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  19. Without actual expansion, prove that the following determinants vanish...

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  20. Without expanding, prove that Delta = abs{:(x+y, y + z, z+ x),(z, x ,...

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  21. Without expanding, prove that : |{:(1, bc, a(b+ c) ),(1, ca, b ( c+ a)...

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