# 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