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Measure of central tendency and dispersion

Sure! Probability and statistics are two interconnected fields of mathematics that deal with the analysis and interpretation of data. A fundamental aspect of both of these fields is the concept of measures of central tendency and measures of dispersion. Measures of central tendency refer to the summary statistics that describe the most typical or representative…

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Diagonal

A matrix is said to be diagonal if all its non-diagonal elements are zero. In other words, a diagonal matrix is a square matrix where all the elements outside the main diagonal are zero. The main diagonal of a matrix is the set of elements that runs from the top-left corner to the bottom-right corner…

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Inverse of a square matrix of order up to three

The inverse of a square matrix A of order n is denoted by A^-1 and is defined as a matrix such that the product of A and A^-1 is the identity matrix of the same order, i.e., AA^-1 = I_n. For a square matrix A of order 2, its inverse is given by the formula:…

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Determinant of a square matrix of order up to three

The determinant of a square matrix of order up to three can be calculated as follows: For a 1×1 matrix: The determinant of a 1×1 matrix is simply the value of the only element in the matrix. For a 2×2 matrix: The determinant of a 2×2 matrix is calculated as follows: |a b| |c d|…

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Matrices Elementary row and column transformations

Matrices are mathematical objects consisting of rows and columns of numbers. They are commonly used in many fields of mathematics, physics, engineering, and computer science. One of the most important concepts in matrix theory is the idea of elementary row and column transformations. These are operations that can be performed on a matrix to transform…

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Transpose of a matrix

In linear algebra, the transpose of a matrix is an operation that flips the matrix over its diagonal, reflecting its rows and columns. The transpose of a matrix A is denoted by A^T. To compute the transpose of a matrix, you simply write the rows of the matrix as columns, and the columns as rows.…

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Multiplication by a scalar and product of matrices

Multiplication by a scalar: Multiplying a matrix by a scalar means multiplying every entry of the matrix by that scalar. For example, if A is a matrix and k is a scalar, then the product kA is obtained by multiplying every entry of A by k. Formally, if A = [a_ij] is an m x…

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Matrices Addition

Matrices addition is a mathematical operation that involves adding two matrices of the same size element-wise. Given two matrices A and B, the sum C=A+B is obtained by adding the corresponding elements of A and B: C(i,j) = A(i,j) + B(i,j) where C(i,j), A(i,j), and B(i,j) are the elements located at the i-th row and…

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Equality of matrices

Two matrices are said to be equal if they have the same dimensions and their corresponding entries are equal. In other words, if A = [aij] and B = [bij] are two matrices of the same size, then A and B are equal if and only if aij = bij for all i and j.…

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Matrices as a rectangular array of real numbers

A matrix is a rectangular array of numbers, which can be real numbers, complex numbers, or even other mathematical objects such as polynomials. In the case of matrices consisting of real numbers, each entry in the matrix is a real number. A matrix can be represented as a rectangular array of numbers enclosed by brackets.…

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