Ví dụ
Bước 1
Bước 1.1
Choose the row or column with the most elements. If there are no elements choose any row or column. Multiply every element in row by its cofactor and add.
Bước 1.1.1
Consider the corresponding sign chart.
Bước 1.1.2
The cofactor is the minor with the sign changed if the indices match a position on the sign chart.
Bước 1.1.3
The minor for is the determinant with row and column deleted.
Bước 1.1.4
Multiply element by its cofactor.
Bước 1.1.5
The minor for is the determinant with row and column deleted.
Bước 1.1.6
Multiply element by its cofactor.
Bước 1.1.7
The minor for is the determinant with row and column deleted.
Bước 1.1.8
Multiply element by its cofactor.
Bước 1.1.9
Add the terms together.
Bước 1.2
Nhân với .
Bước 1.3
Nhân với .
Bước 1.4
Tính .
Bước 1.4.1
Có thể tìm được định thức của một ma trận bằng công thức .
Bước 1.4.2
Rút gọn định thức.
Bước 1.4.2.1
Rút gọn mỗi số hạng.
Bước 1.4.2.1.1
Nhân với .
Bước 1.4.2.1.2
Nhân với .
Bước 1.4.2.2
Trừ khỏi .
Bước 1.5
Rút gọn định thức.
Bước 1.5.1
Nhân với .
Bước 1.5.2
Cộng và .
Bước 1.5.3
Cộng và .
Bước 2
Since the determinant is non-zero, the inverse exists.
Bước 3
Set up a matrix where the left half is the original matrix and the right half is its identity matrix.
Bước 4
Bước 4.1
Multiply each element of by to make the entry at a .
Bước 4.1.1
Multiply each element of by to make the entry at a .
Bước 4.1.2
Rút gọn .
Bước 4.2
Perform the row operation to make the entry at a .
Bước 4.2.1
Perform the row operation to make the entry at a .
Bước 4.2.2
Rút gọn .
Bước 4.3
Multiply each element of by to make the entry at a .
Bước 4.3.1
Multiply each element of by to make the entry at a .
Bước 4.3.2
Rút gọn .
Bước 4.4
Perform the row operation to make the entry at a .
Bước 4.4.1
Perform the row operation to make the entry at a .
Bước 4.4.2
Rút gọn .
Bước 4.5
Multiply each element of by to make the entry at a .
Bước 4.5.1
Multiply each element of by to make the entry at a .
Bước 4.5.2
Rút gọn .
Bước 4.6
Perform the row operation to make the entry at a .
Bước 4.6.1
Perform the row operation to make the entry at a .
Bước 4.6.2
Rút gọn .
Bước 4.7
Perform the row operation to make the entry at a .
Bước 4.7.1
Perform the row operation to make the entry at a .
Bước 4.7.2
Rút gọn .
Bước 4.8
Perform the row operation to make the entry at a .
Bước 4.8.1
Perform the row operation to make the entry at a .
Bước 4.8.2
Rút gọn .
Bước 5
The right half of the reduced row echelon form is the inverse.