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Example-17 :-  Find the area of the triangle whose vertices are (3, 8), (– 4, 2) and (5, 1).

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Example-18 :-  Find the equation of the line joining A(1, 3) and B (0, 0) using determinants and find k if D(k, 0) is a point such that area of triangle ABD is 3sq units.

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  Minor of the element aᵢⱼ is Mᵢⱼ 
  Here a₁₁ = 1. 
  So M₁₁ = Minor of the element a₁₁= 3 
     M₁₂ = Minor of the element a₁₂ = 4 
     M₂₁ = Minor of the element a₂₁ = –2
     M₂₂ = Minor of the element a₂₂ = 1 
        
  Now, cofactor of aᵢⱼ is Aᵢⱼ. 
  So A₁₁ = (–1) ¹⁺¹  M₁₁ = (–1)2 (3) = 3 
     A₁₂ = (–1) ¹⁺²  M₁₂ = (–1)3 (4) = –4 
     A₂₁ = (–1) ²⁺¹  M₂₁ = (–1)3 (–2) = 2 
     A₂₂ = (–1) ²⁺²  M₂₂ = (–1)4 (1) = 1 
   

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Example-22 :-  Find minors and cofactors of the elements of the determinant

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  Now a₁₁ = 2, a₁₂ = –3, a₁₃ = 5;  A₃₁ = –12, A₃₂ = 22, A₃₃ = 18 
  So a₁₁ A₃₁ + a₁₂ A₃₂ + a₁₃ A₃₃ = 2 (–12) + (–3) (22) + 5 (18) = –24 – 66 + 90 = 0
   

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Example-26 :-  where I is 2 × 2 identity matrix and O is 2 × 2 zero matrix. Using this equation, find A^-1.

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Example-27 :-  Solve the system of equations :
2x + 5y = 1
3x + 2y = 7

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Example-28 :-  Solve the following system of equations by matrix method.
3x – 2y + 3z = 8
2x + y – z = 1
4x – 3y + 2z = 4

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Example-29 :-  The sum of three numbers is 6. If we multiply third number by 3 and add second number to it, we get 11. By adding first and third numbers, we get double of the second number. Represent it algebraically and find the numbers using matrix method.

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