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Prove that |[[x,y,z],[x^2,y^2,z^2],[x^3,...

Prove that `|[[x,y,z],[x^2,y^2,z^2],[x^3,y^3,z^3]]|= xyz (x-y)(y-z)(z-x)`

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Without expanding, prove the following |(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=xyz(x-y)(y-z)(z-x)

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Prove that: {:|(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=|(x,x^2,x^3),(y,y^2,y^3),(z,z^2,z^3)| = xyz(x-y(y-z)(z-x)

Using the properties of determinants, prove that : |[[a+x,y,z],[x,a+y,z],[x,y,a+z]]|=a^2(a+x+y+z)

Using the properties of determinant, show that : |[1,x+y,x^2+y^2],[1,y+z,y^2+z^2],[1,z+x,z^2+x^2]| = (x-y)(y-z)(z-x)

Prove that : |[x+y+z,-z,-y],[-z, x+y+z, -x],[-y,-x,x+y+z]|= 2(x+y)(y+z)(z+x)

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BETTER CHOICE PUBLICATION-DETERMINANTS -ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )
  1. Without expanding the determinant, show that : (frac{1}{a}+frac{1}{b}+...

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  2. Prove that |[[a,b,c],[a^2,b^2,c^2],[a^3,b^3,c^3]]|= abc (a-b)(b-c)(c-a...

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  3. Prove that |[[x,y,z],[x^2,y^2,z^2],[x^3,y^3,z^3]]|= xyz (x-y)(y-z)(z-x...

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  4. Solve by matrix method : x+y = 3 , y +z =4 , z + x =5

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  5. Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

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  6. By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+...

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  7. Solve the following system of linear equations by matrix method : 2x +...

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  8. Solve the following system of linear equations by matrix method : 2x -...

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  9. If A= [[4,1,1],[1,4,1],[1,1,4]], then show that |2A| = 8 |A|.

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  10. If A= [[2,1,1],[1,2,1],[1,1,2]], then show that |4A| = 64 |A|.

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  11. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

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  12. Using the properties of determinant, show that : |[1,a+b,a^2+b^2],[1,b...

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  13. Prove that : |[a+b+c,-c,-b],[-c, a+b+c, -a],[-b,-a,a+b+c]|= 2(a+b)(b+c...

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  14. Using the properties of determinant, show that : |[1,x+y,x^2+y^2],[1,y...

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  15. Find the value of k’ if the area of the triangle is 4 sq. units and ve...

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  16. Using matrix method , solve the equations x-y+z=4 2x+y-3z =0 x+y...

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  17. Solve by matrix method 2x + 3y +3z = 5 x -2y + z = -4 3x - y -...

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  18. Solve by matrix method : x + 2y + z = 7, x + 3z= 11, -3y + 2x = 1.

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  19. Without expanding, prove the following |(a,b,c),(a^2,b^2,c^2),(bc,c...

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  20. Solve the following system of linear equations by matrix method : 2x -...

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