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linear algebra

37 posts

Cramer's Rule (Practice Problems)

Last Updated: 21 July 2026

Cramer's Rule is a method for solving a system of linear equations using determinants. It is applicable only when the system has the same number of equations as unknowns a...read more

Augmented Matrix (Practice Problems)

Last Updated: 21 July 2026

An augmented matrix is a matrix that combines the coefficients of a system of linear equations with the constants on the right-hand side. It provides a compact way to repr...read more

Practice Questions on Eigenvalues and Eigenvectors

Last Updated: 21 July 2026

Eigenvalues and eigenvectors are special numbers and vectors associated with a matrix. They describe directions that do not change direction when a matrix transforms them—...read more

Practice Questions on Linear Equations

Last Updated: 21 July 2026

A linear equation is an equation in which each variable has a power of 1 and the graph of the equation is a straight line.Solved ExamplesExample 1: Solve 2x = 3(x + 4)Sol...read more

Linear Equations

Linear Algebra Practice Problems

Last Updated: 21 July 2026

Linear algebra is the branch of mathematics that studies vectors, matrices, and linear equations. It provides the mathematical tools to solve systems of equations and desc...read more

Linear Transformation

Last Updated: 22 June 2026

A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. It transforms vectors while mai...read more

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Introduction to Vector Spaces

Last Updated: 15 May 2026

A vector space V over a field F is a collection of vectors that is closed under vector addition and scalar multiplication. These operations satisfy certain axioms that ens...read more

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Introduction to Linear Algebra

Last Updated: 21 July 2026

Linear algebra is the branch of mathematics that studies vectors, matrices, and linear equations and how they interact. It’s about solving systems like the following:\begi...read more

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Matrices- PYQs | Engineering Mathematics

Last Updated: 05 September 2025

In examinations, questions on matrices are considered very important. Most PYQs are based on definitions, basic operations, and special properties of matrices. To solve su...read more

Engineering Mathematics

Diagonalization of a Matrix

Last Updated: 25 September 2026

The process of converting a square matrix into diagonal form using a similarity transformation is called diagonalization. A matrix A is diagonalizable if there exists an i...read more

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Complex Matrices

Last Updated: 26 August 2025

A complex matrix is made up of complex numbers in the form x + iy, where i = √-1.A complex matrixA∈ Cm×nhas entriesaij = Real(aij) + i⋅Imaginary(aij) A complex matrix is ...read more

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Gauss Elimination Method

Last Updated: 18 June 2026

The Gaussian Elimination Method is a fundamental algorithm in linear algebra used to solve systems of linear equations.By transforming a system into an upper triangular ma...read more

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Linear Algebra in Computer Science

Last Updated: 05 August 2025

Linear algebra is a core mathematics discipline that has a fundamental role in many areas of computer science. It forms the mathematical foundation for numerous algorithms...read more

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LMNs -Linear Algebra

Last Updated: 23 July 2025

Linear algebra isthe study of linear combinations. It is the study of vector spaces, lines and planes, and some mappings that are required to perform the linear transforma...read more

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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...read more

School Learning

Matrix and Determinant

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