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

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

If a, b, c are positive and unequal show that value of the determinant Delta=|[a, b, c],[ b, c, a],[ c, a, b]| is negative.

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

If the product abc =1, then the value of the determinant |{:( -a ^(2), ab, ac),( ba, -b ^(2), bc),(ac, bc,-c ^(2)):}| is

Without expanding the determinant, Prove that |[a,a^2, bc],[b,b^2,ca],[c,c^2,ab]|= |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

Using properties of determinants prove the following. abs[[1,a,bc],[1,b,ca],[1,c,ab]]=(a-b)(b-c)(c-a)

The value of the determinant |(bc,ac,ab),(a,b,c),(a^(3),b^(3),c^(3))| is a)(a + b + c) b)a + b + c -ab c) (a^(2) - b^(2))(b^(2) - c^(2)) (c^(2) - a^(2)) d) a^2+b^2+c^2

By using the properties of determinants,prove that |[a^2+1,ab ,ac],[ab,b^2+1,bc],[ca ,cb,c^2+1]|=1+a^2+b^2+c^2

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

V PUBLICATION-DETERMINANT-QUESTION BANK
  1. Solve the following system of equations using matrix method. 2 x+5 y=1...

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  2. Find the minors and cofactors of a(11), a(1 2) and a(13) of the matrix...

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  3. Let |A|=|[x1, x2, x3],[ y1, y2, y3],[ z1 , z2, z3]|.Expand |A| ...

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  4. Evaluate the determinant of A=[[3, -1, 2],[ 1, 2, -1],[ 4, 0, ...

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  5. Evaluate the determinant |[27, 2, 3],[ 45, 5, 5],[ 36, 9, 4]|

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

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

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  8. Evaluate the determinant of 'A=[[1, 2],[ 3, 4]]'

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  9. Evaluate the determinant of A=[[1 , 3 , 2],[ 2, 0, 1 ],[ 3 , 4, 3]...

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  10. Find the minors and co-factors of the elements 1,-3 and 4 in Delta=|[2...

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  11. Without expanding, evaluate |[2, 1, 5],[ -3, -1, 4],[ 6, 2, -8...

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

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

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  14. If b ne c and |[a , a^2, 1+a^3],[ b, b^2, 1+b^3],[ c, c^2, 1+ c...

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  15. If a, b , c are in A.P show that |[x+1, x+2, x+a],[ x+2, x+3, x+b...

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  16. If A=[[1, 2],[ 3 , 4]], find A^(-1)

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  17. If A=[[1, 1],[ 1 , 2]], verify the (adj A)^(-1) =adj(A^(-1))

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  18. Find inverse of the matrix A=[[cos alpha, -sin alpha, 0 ],[ sin alph...

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  19. For the matrices A=[[-1, 2],[ 3, 4]] and B=[[2, 5],[ 3, 6]], ver...

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  20. Show that [[1 , -tan theta ],[ tan theta, 1]][[1, tan theta],[ -tan...

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