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If A(x1, y1), B(x2, y2) and C(x3, y3) ar...

If `A(x_1, y_1), B(x_2, y_2)` and `C(x_3, y_3)` are vertices of an equilateral triangle whose each side is equal to 'a', then prove that, `|[x_1, y_1, 2 ],[ x_2, y_2, 2],[ x_3, y_3, 2]|^2=3 a^4`

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V PUBLICATION-DETERMINANT-QUESTION BANK
  1. If x, y, z are non zero real numbers, then find the inverse of matrix ...

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  2. Let A = [[1,Sintheta,1],[-Sintheta,1,Sintheta],[-1,-Sintheta,1]], wher...

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  3. If A(x1, y1), B(x2, y2) and C(x3, y3) are vertices of an equilateral t...

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  4. Solve the following system of equations using matrix method. 2 x+5 y=1...

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  5. If [[2,5],[-3,7]]xxA=[[17,-1],[47,-13]] then Find the 2x2 matrix A.

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  6. Let A=[[1 , 4, 0],[ -1, 2, 2],[ 0, 0, 2]] i) is A singular? i...

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  7. Solve the following system of equations using matrix method. 2 x+5 y=1...

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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