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Evaluate : triangle = |[1,a,bc],[1,b,ca]...

Evaluate : `triangle = |[1,a,bc],[1,b,ca],[1,c,ab]|`

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Prove that |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|= 0

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

Find the minors and cofactos of each entry of the first column of the matrix A ad hence find the value of the determinant in each case: A = [(1,a,bc),(1,b,ca),(1,c,ab)]

Find the minor and co-factor of each element of the first column of the following determinants: {:|(1,a,bc),(a,b,ca),(1,c,ab)| Hence or otherwise evaluate them.

Prove that: {:|(1,a,bc),(1,b,ca),(1,c,ab)|=(a-b)(b-c)(c-a)

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

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

Without actual expansion, prove that the following determinants vanish: {:|(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)|

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)

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

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

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

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

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

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

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  7. Prove that : |[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^2(3y+k).

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  8. Solve by using matrix method, 2x - 3y + 5z = 16, 3x +2y-4z=-4, x + y -...

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  9. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/(...

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  10. Evaluate : triangle = |[1,a,bc],[1,b,ca],[1,c,ab]|

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  11. Using determinant , find the area of triangle with verticles (1,0) ,...

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  12. Using determinants , find the area of triangle with vertices (0,0), ...

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  13. Solve the following system of linear equations by matrix method: x - y...

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

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  15. Solve by matrix method 2/x + 3/y + 10/z = 4 , 4/x - 6/y + 5/z = 1 , ...

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  16. Show that: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

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  17. Without expanding show that following : |[a,a+b,a+b+c],[2a,3a+2b,4a+3b...

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

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  19. Solve the following equation by Matrix Method, 1/x - 1/y +2/z =7, 3/x ...

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  20. By using properties of determinants, show that : |[1,1,1],[a,b,c],[a^...

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