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Prove that |[[a,b,c],[a^2,b^2,c^2],[a^3,...

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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Using the properties of determinants show that : |[[1,1,1],[a^2,b^2,c^2],[a^3,b^3,c^3]]|=(a-b)(b-c)(c-a)(ab+bc+ca) .

Prove that: {:|(a^2,a,b+c),(b^2,b,c+a),(c^2,c,ab)| = -(a+b+c)(a-b)(b-c)(c-a)

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

Using properties of determinants, prove that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]| = 3(a+b+c)(ab+bc+ca)

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

Prove the following identities : |{:(a,a^(2),a^(3)),(b,b^(2),b^(3)),(c,c^(2),c^(3)):}|=abc(a-b)(b-c)(c-a) .

Without expanding, prove the following |(1,a,a^3),(1,b,b^3),(1,c,c^3)|=(a-b)(b-c)(c-a)(a+b+c)

Prove that: |[a+b, b+c, c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]|=2|[a,b,c],[b,c,a],[c,a,b]|

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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