91影视

Matrix is a set of numbers arranged in rows and columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an 鈥�m by n 鈥� matrix, written 鈥� $m脳n$.鈥�

If C is a $2脳2$matrix whose entries are all -1 or 1 , then $detB$can only be $-2,0$, or 2 .

Using the Laplace expansion along the first row, we conclude that for a $3脳3$ matrix B with the same property, $\det B$can only be $-6,-4,-2,0,2,4$, or 6 .

Lastly, also using the Laplace expansion along the first row, we can see that for a $4脳4$matrix A, also containing this very same property, using several other properties of the determinant, we conclude that detA indeed must be divisible by 8