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Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],...

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

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Prove that: |[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]|=4a^2b^2c^2

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Prove that: |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|= 2(a+b+c)^3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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