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

find determinant of` |(1, omega, omega^(2)),(omega, omega^(2),1),(omega^(2),1,omega)|=`

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(1+omega-omega^(2))(1-omega+omega^(2))

If omega is a cube root of unit, then Delta=|(x+1,omega, omega^(2)),(omega, x+omega^(2),1),(omega^(2),1,x+omega)|=

If omega is complex cube root of 1 then S.T [(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega)]=0

If 1, omega, omega^(2) are the cube roots of unity then Delta=|(1,omega^(n),omega^(2n)),(omega^(n),omega^(2n),1),(omega^(2n),1,omega^(n))|=

(1-omega+omega^(2))^(7)+(1+omega-omega^(2))^(7)

(1-omega+omega^(2))^(6)+(1-omega^(2)+omega)^(6)

(1- omega + omega^(2))^(7) + (1 + omega - omega^(2))^(7) =

(1-omega)(1-omega^(2))(1-omega^(4))(1-omega^(5))(1-omega^(7))(1-omega^(8))

If omega is a cube root of unity , then |{:( 1 , omega , 2 omega^(2)) , (2 , 2omega^(2) , 4 omega^(3)) , (3 , 3 omega^(3) , 6 omega^(4)):}| =

(1+omega)(1+omega^(2))(1+omega^(3))(1+omega^(4))(1+omega^(5))......(1+omega^(3n))

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-MATRICES -SOLVED PROBLEMS
  1. 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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  2. 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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  3. find determinant of |(1, omega, omega^(2)),(omega, omega^(2),1),(omega...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. The number of nontrivial solutions of the system: x-y+z=0, x+2y=0, 2x+...

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  19. Theorem: Matrix multiplication is associative, i.e., if conformability...

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  20. Theorem : Matrix multiplication, is distri-butive over matrix addition...

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