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Solve [[x+a,b,c],[a,x+b,c],[a,b,x+c]]=0...

Solve `[[x+a,b,c],[a,x+b,c],[a,b,x+c]]=0`

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Factorize the following. [[x+a,b,c],[b,x+c,a],[c,a,x+b]]

Prove the following: [[1,1,1],[a,b,c],[a^3,b^3,c^3]] =(b-c)(c-a)(a-b)(a+b+c)

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The system of equations a_1x+b_1y+c_1z=0 a_2x+b_2y+c_2z=0 a_3x+b_3y+c_3z=0 [[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]]=0

Write the number of solution of the following system of equation. a_1x+b_1y+c_1z=0 a_2x+b_2y+c_2z=0 a_3x+b_3y+c_3z=0 and [[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]] =0

USHA PUBLICATION-MATRICES DETERMINANTS PROBABILITY -EXERCISE
  1. If A and B are two square matrices of same order, then (A+B)^2=A^2+2AB...

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  2. 1.Solve for x: abs ((1,1,x),(p+1,p+1,p+x),(3,x+1,x+2))=0

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  3. Solve [[x+a,b,c],[a,x+b,c],[a,b,x+c]]=0

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  4. If A+B+C = pi, prove that [[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,c...

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  5. Without expanding,show that the following determinant vanishes. abs((2...

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  6. Without expanding,show that the following determinant vanishes. abs ((...

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  7. Without expanding,show that the following determinant vanishes. abs((b...

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  8. Without expanding,show that the following determinant vanishes. abs((6...

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  9. Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

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  10. If a, b and c are all positive real, then prove that minimum value of ...

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  11. Show that: abs((a,a^2,a^3),(b,b^2,b^3),(c,c^2,c^3))=abc(a-b)(b-c)(c-a)

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  12. Prove that: |[a, b, c],[a-b, b-c, c-a ], [b+c, c+a, a+b]|= a^3+b^3+c^3...

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  13. Solve by cramer's rule :2x+3y=6, 4x+6y=12

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  14. If A=[[ 3,-5,],[-4,2,]],show that A^2-5A-14I=O,where I is a unit matri...

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  15. Find the matrix B,if B^2=[[16,0,],[0,16,]].

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  16. If A=[[1,2,],[3,4,]],B=[[-2,3,],[-1,2,]],show that (A+B)^T=A^T+B^T.

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  17. If A=[[2,0,3,],[3,4,5,]],B=[[3,-1,2,],[0,2,3,]]and c=[[2,-3,0,],[1,4,5...

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  18. If A=[[1,2,],[3,4,]],B=[[-2,3,],[-1,2,]],show that (A+B)^T=A^T+B^T.

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  19. If A=[[2,0,3,],[3,4,5,]],B=[[3,-1,2,],[0,2,3,]]and c=[[2,-3,0,],[1,4,5...

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  20. Find the matrix A if A^2=[[17,8,],[8,17,]].

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