pöördmaatriksiga

Pöördmaatriksiga is a term that translates from Estonian to "with inverse matrix." In linear algebra, an inverse matrix, denoted as A⁻¹, is a matrix that when multiplied by the original matrix A, results in the identity matrix. This means that for a square matrix A and its inverse A⁻¹, the product A * A⁻¹ = I, where I is the identity matrix. Not all square matrices have an inverse; only invertible matrices possess an inverse. A matrix is invertible if and only if its determinant is non-zero. The concept of an inverse matrix is fundamental to solving systems of linear equations. If a system can be represented in matrix form as Ax = b, where A is the coefficient matrix, x is the vector of unknowns, and b is the constant vector, then multiplying both sides by the inverse of A (if it exists) yields x = A⁻¹b. This provides a direct solution for the unknown vector x. The calculation of an inverse matrix can be performed using various methods, including Gaussian elimination or by using the adjugate matrix. The existence and uniqueness of an inverse matrix are crucial properties in many areas of mathematics, physics, and engineering.