TOPICS

Formulae

Determinants

1. Determinant of a matrix 1x1 order A = [a₁₁]1×1 is given by |a₁₁| = a₁₁ 2. Determinant of a matrix 2x2 order 3. Determinant of a matrix 3x3 order

1. The area of a triangle whose vertices are (x₁, y₁), (x₂, y₂) and (x₃, y₃), is given by the expression Area of triangle = 1/2[x₁(y₂–y₃) + x₂ (y₃–y₁) + x₃ (y₁–y₂)].

1. The adjoint of a square matrix A = [aᵢⱼ]n × n is defined as the transpose of the matrix [Aᵢⱼ]n × n, where Aᵢⱼ is the cofactor of the element aᵢⱼ. Adjoint of the matrix A is denoted by adj A. 2. Inverse of matrix A, A^{-1}= 1/|A| x adj(A)

1. AX = B or A^{-1}(AX) = A^{-1}B (premultiplying by A^{-1}) or (A^{-1}A) X = A^{-1}B (by associative property) or IX = A^{-1}B or X = A^{-1}B

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