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Using the properties of determinants sho...

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

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

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

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) .

Using the properties of determinants, show that |(1+a,1,1),(1,1+b,1),(1,1,1+c)|=abc+bc+ca+ab

Using properties of determinant , show that : |{:(a,b,c),(a^(2),b^(2),c^(2)),( bc,ca,ab):}|=(ab+bc+ca)(a-b)(b-c)(c-a)

Using the property of determinants and without expanding , prove that: |[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b]| = 0

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

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

BETTER CHOICE PUBLICATION-DETERMINANTS -ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )
  1. Solve |(x+1,2,3),(3,x+2,1),(1,2,x+3)|=0

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  2. Solve by matrix method 3/x+4/y+7/z=14 2/x-1/y+3/z=4 1/x+2/y-3/z=...

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  3. Using the properties of determinants show that : |[[-bc,b^2+bc,c^2+bc]...

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  4. Using the properties of determinants show that : |[[1,1,1],[a^2,b^2,c^...

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  5. Using the properties of determinants show that : |[[1, a^2+bc, a^3],[1...

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  6. Using matrices , solve the following system of linear equations 5x -...

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

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

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  9. 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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  10. 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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  11. Solve by matrix method : x+y = 3 , y +z =4 , z + x =5

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

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

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

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

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

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

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

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

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  20. 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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