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Show that |{:(1,a,a^2),(1,b,b^2),(1,c,c^...

Show that `|{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)`

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The correct Answer is:
(a-b)(b-c)(c-a)
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S.T |(1,a,a^2),(1,b,b^2),(1,c,c^2)| = (a-b)(b-c)(c-a) .

Show that |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}| =(a-b)(b-c)(c-a)(ab+bc+ca)

Show that |{:(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab):}|=0

If Delta=|(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|=k(a-b)(b-c)(c-a) then k=

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

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

|(1,a,a^(2)+bc),(1,b,b^(2)+ac),(1,c,c^(2)+ab)|=k(a-b),(b-c), (c-a) then k =

Show that |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3

Match the following from List - I to List - II {:("List-I","List-II"),((I)|{:(1,1,1),(a,b,c),(bc,ca,ab):}|=,(a)(a-b)(b-c)(c-a)),((II)|{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3)):}|=,(b)(a-b)(b-c)(c-a)abc),((III)|{:(1,1,1),(a,b,c),(a^(3),b^(3),c^(3)):}|=,(c)(a-b)(b-c)(c-a)(a+b+c)):}

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):}|

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-MATRICES -SOLVED PROBLEMS
  1. If [(0,4,-2),(-4,0,8),(2,-8,x)] is a skew symmetric matrix then find t...

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  2. For any n xx n matrix A, prove that A can be uniquely expressed as a s...

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  3. Show that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)

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  4. Show that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=2|{:(a,b,c),...

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  5. Show that |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}| =(a-b)(b-c)(c-a)(a...

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  6. find determinant of |(1, omega, omega^(2)),(omega, omega^(2),1),(omega...

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  7. Show that |{:(a-b-c," "2a," "2a),(" "2b,b-c-a," "2b),(" "2c," "2...

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  8. Show that the determinant of skew - symmetric matrix of order three is...

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  9. Fiind the valueof x if: |{:(x-2, 2x-3, 3x-4),(x-4, 2x-9, 3x-16),(x-8...

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  10. Find the Adjoint and Inverse of the matrix A = [(1,2),(3,-5)]

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  11. Find the adjoint and the inverse of the matrix A=[{:(1,3,3),(1,4,3),(1...

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  12. Show that the matrix A=[{:(1,2,1),(3,2,3),(1,1,2):}] is non-singular a...

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  13. Find the rank of A=[{:(0,1,2),(1,2,3),(3,2,1):}] using elementary tran...

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  14. Find the rank of A=[{:(1,2,0,-1),(3,4,1,2),(-2,3,2,5):}] using element...

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  15. Apply the test of rank to examine whether the following equations are ...

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  16. Solve the following system of equations by using Cramer,s ruel . 3x...

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  17. Solve the equations 3x+4y+5z=18,2x+y+8z=13,5x-2y+7z=20 by matrix inver...

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  18. Solve the following system of equations by using Cramer,s ruel . 3x...

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  19. Solve the system of equations 2x+4y-z=0,x+2y+2z=5,3x+6y-7z=2 by Gauss ...

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  20. Solve the following- system of equations, 2x + 5y + 6z = 0, x - 3y + 8...

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