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Without expanding the determinant prove the following. |[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]|=0

Evaluate Delta=|[1, a, bc],[ 1, b, c a],[ 1, c, 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)

Find the value of the determinant |[1, a, b+c],[ 1, b, c+a],[ 1, c, a+b]|

If a, b and c are distinct reals and the determinant |{:(a ^(3) +1, a ^(2) , a ),( b ^(3) +1, b ^(2) , b ),( c ^(3) +1, c ^(2), c):}|= 0, then the product abc is

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

|(1,a,b+c),(1,b,c+a),(1,c,a+b)| =

A=[[0 , 6 , 7 ],[ -6, 0 , 8 ],[ 7, -8, 0]] , B=[[0, 1 ,1],[ 1 , 0 ,2],[ 1 ,2 ,0]] , C=[[2 ],[ -2],[ 3]] Calculate AC , B C and (A+B) C . Also, verify that (A+B) C=A C+B C

If (b + c) (y + z) - ax = b - c, (c + a) (z + x) - by = c - a and (a + b) (x + y) - cz = a - b , where a + b + c ne 0, then x is equal to a) (c + b)/(a + b + c) b) (c - b)/(a + b + c) c) (a - b)/(a + b + c) d) (a + b)/(a + b + c)

V PUBLICATION-DETERMINANT-QUESTION BANK
  1. Without expanding the determinant prove the following. |[a-b,b-c,c-a...

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  2. Evaluate |[2, 7, 65],[ 3, 8, 75],[ 5, 9, 86]|=0

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

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  4. Without expanding the determinant prove the following. |[b+c,q+r,y+z...

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  5. By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],...

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  6. By using properties of determinants, prove that |[-a^2,ab,ac],[ba,-b^...

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  7. 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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  8. By using properties of determinants, prove that |[x,x^2,yz],[y,y^2,zx...

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  9. Prove that abs[[y+k,y,y],[y,y+k,y],[y,y,y+k]]=k^2(3y+k)

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  10. By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+...

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

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  12. Prove |[1+a^2-b^2, 2 a b, -2 b],[ 2 a b, 1-a^2+b^2, 2 a],[ 2 b,...

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  13. By using the properties of determinants,prove that |[a^2+1,ab ,ac],[a...

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  14. Let A be a square matrix of order 2x2 thenabs[KA] is equal to

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  15. Which of the following is correct? a)Determinant is a square matrix ...

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  16. Find the area of the triangle whose vertices are (3,8),(-4,2)and (5,1)

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  17. Find the equation of the line joining A(1,3) and B(0,0) using determin...

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  18. Find the area of the triangle with vertices at (1,0),(6,0),(4,3) using...

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  19. Using the property of determinants,show that the points A(a,b+c),B(b...

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  20. Find the values of k if area of triangle is 4 sq. units and vertices a...

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