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Using the properties of determinant, sho...

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)`

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By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+z+2x,y],[z,z,z+x+2y]| = 2(x+y+z)^3

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)

Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)| = (x-y)(y-z)(z-x)

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Using properties of determinants , prove that |(x^2+1,xy,zx),(xy,y^2+1,yz),(zx,yz,z^2+1)|=1+x^2+y^2+z^2

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BETTER CHOICE PUBLICATION-DETERMINANTS -ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )
  1. Using the properties of determinant, show that : |[1,a+b,a^2+b^2],[1,b...

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

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

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

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

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

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

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

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  10. Solve by matrix method 3x - 2y + 3z =8 2x + y - z =1 4x -3y +2z...

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  11. Solve by matrix method 2x +y +z=1 x-2y-z =3//2 3y-5z =9

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  12. Prove that : |[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^2(3y+k).

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  13. Solve by using matrix method, 2x - 3y + 5z = 16, 3x +2y-4z=-4, x + y -...

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  14. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/(...

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  15. Evaluate : triangle = |[1,a,bc],[1,b,ca],[1,c,ab]|

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  16. Using determinant , find the area of triangle with verticles (1,0) ,...

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  17. Using determinants , find the area of triangle with vertices (0,0), ...

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  18. Solve the following system of linear equations by matrix method: x - y...

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

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  20. Solve by matrix method 2/x + 3/y + 10/z = 4 , 4/x - 6/y + 5/z = 1 , ...

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