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Show that abs[[a+b,b+c,c+a],[b+c,c+a,a+b...

Show that `abs[[a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]]=2abs[[a,b,c],[b,c,a],[c,a,b]]`

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Show that abs [[1,a,bc],[1,b,ac],[1,c,ab]]=(a-b)(b-c)(c-a)

S.T abs[[x+a,b,c],[a,x+b,c],[a,b,x+c]]=x^2(x+a+b+c)

Show that Delta=abs[[-a^2,ab,ac],[ba,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

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

prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

prove |[1, b c, a(b+c)],[ 1, c a, b(c+a)],[ 1, a b, c(a+b)]|=0

Evaluate |[1,1,1],[a,b,c],[b+c,c+a,a+b]|

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

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BODY BOOKS PUBLICATION-DETERMINANTS-EXERCISE
  1. Using properties of determinants prove the following. abs[[a-b-c,...

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  2. Given Delta=[(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)] Express given ...

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  3. Show that abs[[a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]]=2abs[[a,b,c],...

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  4. Find the equation of line joining (1,2) and (3,6) using determinants.

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  5. Prove that |[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]| is...

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  6. Prove that |[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]| is...

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  7. using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],...

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  8. If A=[[2,-3,5],[3,2,-4],[1,1,-2]] Find A^-1

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  9. If A=[[2,-3,5],[3,2,-4],[1,1,-2]] Using it solve the system of equat...

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  10. prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

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  11. if A=[[1,-1,2],[0,2,-3],[3,-2,4]] B=[[-2,0,1],[9,2,-3],[6,1,-2]] Prov...

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  12. if A=[[1,-1,2],[0,2,-3],[3,-2,4]] B=[[-2,0,1],[9,2,-3],[6,1,-2]] ...

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  13. If A=[[a,1],[1,0]] is such that A^2=I then a equals

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  14. Solve the system of equations x-y+z=4,2x+y-3z=0,x+y+z=2 Using matr...

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  15. The value of abs((x,x-1) , (x+1,x):} is a)1 b)x c)x^2d)0

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  16. Using properties of determinants prove the following. abs[[1,x,x^2...

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  17. Prove that |(1,x,x^3),(1,y,y^3),(1,z,z^3)|=(x+y+z)(x-y)(y-z)(z-y).

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  18. Prove that abs[[1!,2!,3!],[2!,3!,4!],[3!,4!,5!]]=4!

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  19. Solve the system of Linear equations x+2y+z=8,2x+y-z=1,x-y+z=2

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  20. Inverse of the matrix [[0,1,2],[0,1,1],[1,0,2]]

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