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Show that: abs((a,a^2,a^3),(b,b^2,b^3),(...

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

Prove that the following. [[a,a^2,a^3],[b,b^2,b^3],[c,c^2,c^3]] = abc(a-b)(b-c)(c-a)

Prove that abs((a,b,c),(a^2,b^2,c^2),(bc,ca,ab))=(a-b)(b-c)(c-a)(ab+bc+ca)

Prove that |(1, a, a^3),(1, b, b^3),(1, c, c^3)| = (a-b)(b-c)(c-a)(a+b+c).

Prove that abs((-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c))=4(b+c)(c+a)(a+b)

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

Show that abs((2(a+b+c),a,b),(2(a+b+c),b+c+2a,b),(2(a+b+c),a,c+a+2b))=2(a+b+c)^3

USHA PUBLICATION-MATRICES DETERMINANTS PROBABILITY -EXERCISE
  1. 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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  2. If a, b and c are all positive real, then prove that minimum value of ...

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  3. 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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  4. 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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  5. Solve by cramer's rule :2x+3y=6, 4x+6y=12

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

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

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

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

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

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  13. Verify that (AB)^-1=B^-1A^-1 if A=[[2,3,],[1,-1,]],B=[[0,1,],[3,1,]]

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  14. Verify that (AB)^-1=B^-1A^-1 if A=[[1,2,3,],[4,5,6,],[7,8,9,]],B=[[1,2...

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  15. If A=[[1,-1,1,],[2,-1,0,],[1,0,0,]],then show that A^2=A^-1.

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  16. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

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  17. Show that the matrix A=[[2,3,],[1,2,]]satisfies the equation A^2-4A+I=...

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  18. If A=[{:(costheta,sintheta),(-sintheta,costheta):}], then prove that ...

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  19. Express the matrix A=[[4,2,-3],[1,3,-6],[-5,0,-7]] as the sum of symme...

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  20. Examining consistency and solvability, solve the following equation by...

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