University:
Georgia Southern University
Course:
ENGR 2139 | Numerical Methods
Academic year:

2024
Views:

446

Pages:

25
Author:

Jalen W.

Symmetric matrix A = AT antisymmetric matrix A = -AT Matrix addition and subtraction Matrix multiplication: For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The result matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. Co-Factor Matrix Matrix of Cofactors. A matrix with elements that are the cofactors, term-by-term, of a given square matrix. In linear algebra, the determinant is a scalar value that can be computed from the elements of a square matrix, and which encodes certain properties of the linear transformation described by the matrix. The determinant of a matrix A is denoted det(A), det A, or |A|. The determinant is useful for solving linear equations, capturing how linear transformation change area or volume, and changing variables in integrals. The determinant can be viewed as a function whose input is a square matrix and whose output is a number. Adjoint Matrix is the Transpose of the Co factor Matrix of given original Matrix The identity matrix is a square matrix that has 1's along the main diagonal and 0's for all other entries. This matrix is often written simply as I, and is special in that it acts . like 1 in matrix multiplication Inverse of a Matrix [A] is [B], where [B]=[A]-1 Inverse Matrix, [B]= Solving sets of linear equations using Matrix Crammer’s Rule Gauss elimination method For this system, the augmented matrix (vertical line omitted) is First, multiply row 1 by 1/2: Now, adding −1 times the first row to the second row yields zeros below the first entry in the first column: The third row now says z = 4. Back‐substituting this value into the second row gives y = 1, and back‐substitution of both these values into the first row yields x = −2. The solution of this system is therefore (x, y, z) = (−2, 1, 4).

Symmetric Matrix

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