Matrices

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A matrix is an ordered rectangular array of numbers or functions. The numbers or functions are called the elements or entries of the matrix. Matrices are denoted by capital letters like A, B, C, etc.

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The order of a matrix is written as m × n, where m is the number of rows and n is the number of columns. A matrix with m rows and n columns is called an m × n matrix. For example, if a matrix has 3 ro…

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An m × n matrix contains m × n elements. For example, a 3 × 4 matrix contains 3 × 4 = 12 elements.

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A column matrix is a matrix that has only one column. Its order is m × 1. Example: [2, -1, 5]ᵀ is a column matrix of order 3 × 1.

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A row matrix is a matrix that has only one row. Its order is 1 × n. Example: [3, -2, 0, 7] is a row matrix of order 1 × 4.

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A square matrix is a matrix in which the number of rows equals the number of columns (m = n). It is known as a square matrix of order n. Example: A 2×2 matrix [[1, 2], [3, 4]] is a square matrix of or…

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In a square matrix A = [aᵢⱼ] of order n, the diagonal elements are a₁₁, a₂₂, a₃₃, ..., aₙₙ. These are the elements where the row index equals the column index (i = j).

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A square matrix B = [bᵢⱼ] is a diagonal matrix if all its non-diagonal elements are zero. That is, bᵢⱼ = 0 when i ≠ j. Only the diagonal elements can be non-zero.