Here you will learn properties of determinant of matrix with examples. Let’s begin – Properties of Determinant of Matrix Property 1 : The value of determinant remains unaltered or unchanged, if the rows & columns are inter-changed, e.g. if D = \(\begin{bmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 […]
Properties of Determinant of Matrix Class 12 Read More »
Her you will learn how to find determinants of matrix 4×4 with example. Let’s begin – Determinants of Matrix 4×4 To evaluate the determinant of a square matrix of order 4 we follow the same procedure as discussed in previous post in evaluating the determinant of a square matrix of order 3. If A =
Determinants of Matrix 4×4 with Examples Read More »
Here you will learn how to find determinants of matrix 3×3 with examples. Let’s begin – Determinants of Matrix 3×3 If A = \(\begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix}\) is a square matrix of order 3, then \(a_{11}(a_{22}a_{33} – a_{23}a_{a32})\) – \(a_{12}(a_{33}a_{21}
Determinants of Matrix 3×3 with Examples Read More »
Here you will learn formula for inverse of a matrix and properties of inverse of matrix with example. Let’s begin – Formula for Inverse of a Matrix A square matrix A said to be invertible if and only if it is non-singular (i.e. |A| \(\ne\) 0) and there exists a matrix B such that, AB
Formula for Inverse of a Matrix – Properties, Example Read More »
Here you will learn how to find adjoint of the matrix 2×2 and 3×3, cofactors and its properties with examples. Let’s begin – Adjoint of the Matrix Let A = \([a_{ij}]\) be a square matrix of order n and let \(C_{ij}\) be a cofactor of \(a_{ij}\) in A. Then the transpose of the matrix of
Adjoint of the Matrix (2×2 & 3×3) – Properties, Examples Read More »
Here you will learn how to find trace of matrix, its properties and what is orthogonal matrix with example. Let’s begin – Trace of Matrix The sum of the elements of the square matrix A lying along the principal diagonal is called the trace of A i.e (tr(A)). Thus if A = \([a_{ij}]_{n\times n}\), then
How to Find Trace of Matrix – Properties and Example Read More »
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 &
Symmetric and Skew Symmetric Matrices Read More »
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,
What is Transpose of Matrix – Definition and Example Read More »
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)
Properties of Multiplication of Matrices Read More »
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
Multiplication of Matrices – Examples and Definition Read More »
