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By using properties of determinants, sh...

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`

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The correct Answer is:
`x=1,y=2,z=-1`
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BETTER CHOICE PUBLICATION-DETERMINANTS -ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )
  1. Solve by matrix method : x+y = 3 , y +z =4 , z + x =5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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