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Without expanding the determinant, show ...

Without expanding the determinant, show that : `(frac{1}{a}+frac{1}{b}+frac{1}{c}+1)` is a factor of : `|[[1+a,1,1],[1,1+b,1],[1,1,1+c]]|`

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BETTER CHOICE PUBLICATION-DETERMINANTS -ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )
  1. Using matrices , solve the following system of linear equations 5x -...

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

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  3. Without expanding the determinant, show that : (frac{1}{a}+frac{1}{b}+...

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  4. 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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  5. 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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  6. Solve by matrix method : x+y = 3 , y +z =4 , z + x =5

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

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

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

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

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

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

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

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

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

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

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

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

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

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