Posts for Tag: Matrices and Determinants

Operations with matrices

Two matroces A and B are equal if, and only if, they are both of the same shape $mxn$ and corresponding elemts are equal, i.e. $[a_{ij}\ ]=[b_{ij}\ ]$ Two matrices A and B can be added (or subtracted) if, and only if, they have the same shape $mxn$. And in the resultant matrix each ofRead More

Matrices Formulas

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. An $m\ x\ n$ matrix A is a rectangular array of elements (numbers of functions) with m rows and n columns $A=[a_{ij}]=[\table a_11,a_12,…,a_{1n};a_21,a_22,…,a_{2n};…,…,…,…;a_{m1},a_{m2},…,a_{mn}]$ Square matrix is a matrix of order $nxn$ A square matrix $[a_{ij}]$Read More

Properties of Determinants

The value of determinant remains unchanged if rows are changed to columns and columns are changed to rows. $|\table a_1, a_2; b_1, b_2|=|\table a_1, b_1; a_1, b_2|$ If two rows or two columns are interchanged, the sign of the determinant is changed. $|\table a_1, a_2; b_1, b_2|=-|\table b_1, b_2; a_1, a_2|$ If two rows orRead More

Determinants Formulas

In linear algebra, the determinant is a value that can be computed from the elements of a square matrix. The determinant of a matrix A is denoted det(A), det A, or |A|. Matrices: A Elements of a matrix: ai, ai, aij, bij, … aij… Determinant of matrix A: |A| Second order determinant $|A|=|\table a_1,b_1;a_2,b_2|=a_1b_2-a_2b_1$ ThirdRead More