Here you will learn what are symmetric and skew symmetric matrices with examples. Let’s begin – Symmetric and Skew Symmetric Matrices Symmetric Matrix A square matrix A = \([a_{ij}]\) is called a symmetric matrix, if \(A^T\) = A or \(a_{ij}\) = \(a_{ji}\) for all i, j. for example, the matrix A = \(\begin{bmatrix} 3 & …
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Here you will learn what is transpose of matrix with definition and examples. Let’s begin – What is Transpose of Matrix Let A = \([a_{ij}]\) be a \(m\times n\) matrix. Then the transpose of A, denoted by \(A^{T}\) or A’, is an \(n\times m\) matrix such that \((A^T)_{ij}\) = \(a_{ji}\) for all i = 1, …
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Here you will learn properties of multiplication of matrices, positive integral powers of square matrix and matrix polynomial. Let’s begin – Also Read : Multiplication of Matrices – Examples & Definition Properties of Multiplication of Matrices (a) Matrix multiplication is not commutative in general i.e AB \(\ne\) BA. (b) Matrix multiplication is associative i.e. (AB) …
Here you will learn multiplication of matrices with definition and examples. Let’s begin – Multiplication of Matrices Definition : Two matrices A and B are conformable for the product AB if the number of columns in A is same as the number of row in B. Let matrix A is of order \(m\times n\) then m …
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Here you will learn subtraction of matrices with examples. Let’s begin – Subtraction of Matrices Let two matrices A and B of the same order, the subtraction of matrix B from matrix A is denoted by A – B and is defined as A – B = A + (-B). Note : If matrices are not …
Here you will what is matrix and definitions of different types of matrices with examples. Let’s begin – What is Matrix ? A set of mn numbers (real or imaginary) arranged in the form of a rectangular array of m rows and n columns is called an m \(\times\) n matrix (to be read as …
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Here you will learn equality of matrices definition with examples. Let’s begin – Equality of Matrices Definition : Two matrice A = \([a_{ij}]_{m\times n}\) and B = \([b_{ij}]_{r\times s}\) are equal if (i) m = r i.e. the number of rows in A equals the number of rows in B. (ii) n = s i.e the …
Here you will learn scalar multiplication with matrices (multiplicaition of a matrix by a scalar ) and properties of scalar mutiplication. Let’s begin – Scalar Multiplication with Matrices Definition : Let \([a_{ij}]\) be an \(m\times n\) matrix and k be any number called a scalar. Then the matrix obtained by mutiplying every element of A by …
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Here you will learn how to add matrix and properties of addition of matrices with examples. Let’s begin – Addition of Matrices Let A, B be two matrices, each of order \(m \times n\). Then their sum A + B is a matrix of order \(m \times n\) and is obtained by adding the correspoding …
Here you will learn addition theorem of probability for two and three events with statement and proof. Let’s begin – Addition Theorem of Probability For two events : If A and B are two events associated with a random experiment, then P(\(A \cup B\)) = P(A) + P(B) – P(\(A \cap B\)) Proof : Let S …
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