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  Determinants $A = (a_{ij})$ is a square matrix, then the determinant of $A$ is a number. Denoted by: $det(A)$ or $|A|$ Minor of entry $a_{ij}$: $M_{ij}$ Cofactor of entry $a_{ij}$ = $C_{ij} = (-1)^{i+j} M_{ij}$ Formula of $det(A)$: $\sum^n_{j=1} a_{1j} C_{1j} = \sum^n_{j=1} a_{1j}(-1)^{1+j} M_{1j}$  Smart choice!!! Choose the row/ column with most zeros!!! How an operation affects the value of determinant:  Swap the row/column: đổi dấu giá trị det Multiply a row/ column with $\lambda$: nhân $\lambda$ với giá trị det cộng trừ các hàng cột với nhau: det giữ nguyên If a matrix has two equal rows or columns, its determinant = 0. If a matrix has two proportional rows or columns, its det = 0. $A, B$ are two square matrices of the same size: $det(AB) = det(A)*det(B)$ $det(\alpha AB) = \alpha^n*detA*detB$ with $n$ is the rank of the matrices. A minor of A of order k: chỉ những matrix vuông có kích thước k*k trong matrix lớn.  The rank of A được kết luận từ matrix con c...

  MATRICES Zero matrix: all entries in the matrix are zero Main diagonal: all entries on the main diagonal, starting from $a_{11}$ Square matrix of order $n$:   $A_{n*n}$ Diagonal matrix: square matrix with all entries except the main diagonal are zero Triangular matrix:  We have two kinds, this is upper and the reverse is lower Identity matrix: square matrix with 1s on the main diagonal and the remaing are 0s. Tranpose of $A$: $A^T$: when we put all the entries on the rows to the columns and all on the columns to the rows. Elementary Row Operations on matrix $A$: Interchange 2 rows $r_i \leftrightarrow r_j$ Multiply a row through by a nonzero constant: $r_i \to \lambda r_i$ $(\lambda \ne 0)$ Add a constanst times one row to another: $r_i \to r_j + \lambda . r_j$   Leading entry: first non-zero element of each row Row echelon form: <in Vietnamese> phần tử của ma trận hàng dưới sẽ thụt vô so với hàng trên Rank of the matrix: the number of non-zero r...