Примеры
Этап 1
Этап 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.
Этап 1.1.1
Consider the corresponding sign chart.
Этап 1.1.2
The cofactor is the minor with the sign changed if the indices match a position on the sign chart.
Этап 1.1.3
The minor for is the determinant with row and column deleted.
Этап 1.1.4
Multiply element by its cofactor.
Этап 1.1.5
The minor for is the determinant with row and column deleted.
Этап 1.1.6
Multiply element by its cofactor.
Этап 1.1.7
The minor for is the determinant with row and column deleted.
Этап 1.1.8
Multiply element by its cofactor.
Этап 1.1.9
Add the terms together.
Этап 1.2
Умножим на .
Этап 1.3
Умножим на .
Этап 1.4
Найдем значение .
Этап 1.4.1
Определитель матрицы можно найти, используя формулу .
Этап 1.4.2
Упростим определитель.
Этап 1.4.2.1
Упростим каждый член.
Этап 1.4.2.1.1
Умножим на .
Этап 1.4.2.1.2
Умножим на .
Этап 1.4.2.2
Вычтем из .
Этап 1.5
Упростим определитель.
Этап 1.5.1
Умножим на .
Этап 1.5.2
Добавим и .
Этап 1.5.3
Добавим и .
Этап 2
Since the determinant is non-zero, the inverse exists.
Этап 3
Set up a matrix where the left half is the original matrix and the right half is its identity matrix.
Этап 4
Этап 4.1
Multiply each element of by to make the entry at a .
Этап 4.1.1
Multiply each element of by to make the entry at a .
Этап 4.1.2
Упростим .
Этап 4.2
Perform the row operation to make the entry at a .
Этап 4.2.1
Perform the row operation to make the entry at a .
Этап 4.2.2
Упростим .
Этап 4.3
Multiply each element of by to make the entry at a .
Этап 4.3.1
Multiply each element of by to make the entry at a .
Этап 4.3.2
Упростим .
Этап 4.4
Perform the row operation to make the entry at a .
Этап 4.4.1
Perform the row operation to make the entry at a .
Этап 4.4.2
Упростим .
Этап 4.5
Multiply each element of by to make the entry at a .
Этап 4.5.1
Multiply each element of by to make the entry at a .
Этап 4.5.2
Упростим .
Этап 4.6
Perform the row operation to make the entry at a .
Этап 4.6.1
Perform the row operation to make the entry at a .
Этап 4.6.2
Упростим .
Этап 4.7
Perform the row operation to make the entry at a .
Этап 4.7.1
Perform the row operation to make the entry at a .
Этап 4.7.2
Упростим .
Этап 4.8
Perform the row operation to make the entry at a .
Этап 4.8.1
Perform the row operation to make the entry at a .
Этап 4.8.2
Упростим .
Этап 5
The right half of the reduced row echelon form is the inverse.