Matrices

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A matrix is an ordered rectangular array of numbers arranged in rows and columns. The numbers are called elements or entries of the matrix. Horizontal lines are called rows and vertical lines are call…

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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 3 rows and 4 columns has order 3×4 (read as '3 by 4').

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A row matrix is a matrix that has only one row. Example: B = [2 -1 5 3] is a row matrix of order 1×4. In general, a row matrix has order 1×n.

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

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A square matrix is a matrix where the number of rows equals the number of columns. Example: A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] is a square matrix of order 3×3. In general, a square matrix has order…

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An identity matrix is a square matrix where all diagonal elements are 1 and all non-diagonal elements are 0. It is denoted by I. Example: I₂ = [[1, 0], [0, 1]] is a 2×2 identity matrix.

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A null matrix is a matrix where all elements are zero. It is denoted by 0. Example: O = [[0, 0], [0, 0]] is a 2×2 null matrix. It can be of any order m×n.

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A diagonal matrix is a square matrix where all non-diagonal elements are zero. Only the principal diagonal elements can be non-zero. Example: D = [[3, 0, 0], [0, -2, 0], [0, 0, 5]] is a 3×3 diagonal m…