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Matrix and Determinant
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Introduction to Determinants
Last Updated: 09 June 2026
The determinant of a matrix is a scalar value that can be calculated for a square matrix (a matrix with the same number of rows and columns). It serves as a scaling factor...
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Mathematics
Matrix and Determinant
Maths
Properties of Transpose of Matrix
Last Updated: 23 July 2025
The transpose of a matrix is a new matrix that is formed by flipping the original matrix over its diagonal. This operation essentially switches the rows and columns of the...
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How to Multiply a 3 × 3 Matrix with a 3 × 1 Matrix
Last Updated: 23 July 2025
Matrix multiplication is a way to combine two matrices (rectangular arrays of numbers) to create a new matrix.You can only multiply two matrices if the number of columns i...
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linear algebra
Practice Questions on Subtraction of Matrices
Last Updated: 23 July 2025
Subtraction of Matrices is one of the operations that are performed between two matrices. It is similar to addition of matrices. This article provides practice questions o...
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Transformation Matrix
Last Updated: 08 August 2025
Transformation matrices are fundamental in linear algebra and play a key role in areas like computer graphics, image processing, and more. They allow us to apply operation...
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Non Singular Matrix
Last Updated: 24 October 2025
A non-singular matrix (also called an invertible matrix) is a square matrix whose determinant is a non-zero value.It is used to find the inverse of a matrix. The condition...
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How to Find Rank of a 3x3 Matrix
Last Updated: 23 July 2025
Rank of a matrix is equal to the number of linear independent rows or columns in it. The rank of the matrix is always less than or equal to the order of the matrix. In thi...
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Determinant of a Square Matrix
Last Updated: 23 July 2025
Determinant of a square matrix is the scalar value or number calculated using the square matrix. The determinant of square matrix X is represented as |X| or det(X). In thi...
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Rotation Matrix
Last Updated: 23 July 2025
A Rotation Matrix is a type of transformation matrix used to rotate vectors in a Euclidean space. It applies matrix multiplication to transform the coordinates of a vector...
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Methods to Find Rank of a Matrix
Last Updated: 23 July 2025
To find the rank of a matrix find the highest order of the non-zero minor within the matrix. Rank of a matrix in the number that represents the number of non-zeros rows or...
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Practice Problems on Determinant using Elementary Operations
Last Updated: 16 May 2024
Using the properties of determinants and without expanding in Exercise 1 to 7, prove that: Question 1. \begin{vmatrix}x a x+a\\y b y+b\\z c z+c\end{vmatrix}=0 Sol...
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Determinant of 4x4 Matrix
Last Updated: 17 November 2025
The determinant of a matrix is a single numerical value that can be calculated from a square matrix (a matrix with the same number of rows and columns). It tells us import...
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Linear Independence
Last Updated: 25 May 2026
Linear independence is a fundamental concept of linear algebra. It has numerous applications in fields like physics, engineering, and computer science. It is necessary for...
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Inverse of 2x2 Matrix
Last Updated: 07 March 2026
The inverse of a 2 × 2 matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix. It is an important concept in linear algebra and is...
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Rank and Nullity
Last Updated: 23 August 2025
Rank and Nullity are essential concepts in linear algebra, particularly in the context of matrices and linear transformations. They help describe the number of linearly in...
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