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

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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Prove that: |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]|=|[a^2+1,b^2,c^2],[a^2,b^2+1,c^2],[a^2,b^2,c^2+1]|=1+a^2+b^2+c^2

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Without expanding the determinant, prove that |[a,a^2,bc],[b,b^2,ca],[c,c^2,ab]| = |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

Using the properties of determinant, show that : |[1,a+b,a^2+b^2],[1,b+c,b^2+c^2],[1,c+a,c^2+a^2]| = (a-b)(b-c)(c-a)

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BETTER CHOICE PUBLICATION-DETERMINANTS -ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )
  1. Using the properties of determinants, prove that : |[[x+a,b,c],[a,x+b,...

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  2. 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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  3. Solve |(x+1,2,3),(3,x+2,1),(1,2,x+3)|=0

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

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

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

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

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

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

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  11. 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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  12. 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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  13. Solve by matrix method : x+y = 3 , y +z =4 , z + x =5

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

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

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

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

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

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

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

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