Matrices

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A matrix is an ordered rectangular array of elements (numbers, variables, or expressions) arranged in rows and columns. Example: A = [2 3; 4 5] is a 2×2 matrix with: - Row 1: [2, 3] - Row 2: [4, 5] -

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The order of a matrix is written as m×n where: - m = number of rows - n = number of columns For matrix B = [1 2 3; 4 5 6]: - Number of rows = 2 - Number of columns = 3 - Therefore, order = 2×3 Gener

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A square matrix is a matrix where the number of rows equals the number of columns (order n×n). Example: A = [1 2 3; 4 5 6; 7 8 9] is a 3×3 square matrix Principal Diagonal: The diagonal from top-lef

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Row Matrix: A matrix with only one row (order 1×n) Example: R = [2 -1 5 7] (order 1×4) Column Matrix: A matrix with only one column (order m×1) Example: C = [3; -2; 1; 6] (order 4×1) Key Points: - R

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Diagonal Matrix: Square matrix where all non-diagonal elements are zero Example: D = [3 0 0; 0 -2 0; 0 0 5] Scalar Matrix: Diagonal matrix where all diagonal elements are equal Example: S = [4 0 0; 0

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Zero/Null Matrix: A matrix where all elements are zero, denoted by O Example: O₂ₓ₃ = [0 0 0; 0 0 0] Equal Matrices: Two matrices A and B are equal (A = B) if: 1. They have the same order 2. Correspon

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Scalar Multiplication: Multiply each element of the matrix by the scalar If A = [aᵢⱼ] and k is a scalar, then kA = [kaᵢⱼ] Solution: A = [2 -1; 0 4] 3A = 3[2 -1; 0 4] = [3×2 3×(-1); 3×0 3×4]

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Matrix Addition: Add corresponding elements of matrices of the same order Condition: Both matrices must have the same order If A = [aᵢⱼ] and B = [bᵢⱼ], then (A + B) = [aᵢⱼ + bᵢⱼ] Solution: A + B = [