2. Using determinant property transformation,

Multiply one line by another.

A two-line swap

Extract the common factor of a row

This method can be reduced to an upper (lower) triangular determinant.

(The same is true for column transformations.)

Or, if conditions permit, expand the order reduction by one line.

Generally, it is better to find more than 0 rows or more than 0 columns first.

There are many ways to solve the problem, and this is one of them.

1, the second line× (-10) is added to the third line.

2. The second line × (-4) is added to the first line 1.

3. Expand by the first column

(-1)× three-level determinant (the determinant is reduced to three-level determinant, and there is one more-1).

4. The second column × (- 1) is added to the 1 column.

5. The second column × (- 1) is added to the third column.

6. Press the third column.

(-1)×(- 1)× a second-order determinant (the determinant is reduced to a second-order determinant, and one more-1).

7. The second-order determinant can be directly calculated by cross multiplication.

Therefore, the end result is

(- 1)×(- 1)×((-9)×(-34)-(- 17)×(- 18))=0

Of course, this method is not the only way to solve the problem.

1, the second line× (-10) is added to the third line.

2. The second line × (-4) is added to the first line 1.

3. Add the column 1 ×(-2) to the second column.

4. Add the 1× (-2) column to the fourth column.

5. Line 3× (-1) is added to line1.

6. The third column × (- 1) is added to the second column.

7, the third column x (-7) is added to the fourth column.

8. At this time, the oral calculation shows that the second column is directly proportional to the fourth column, and the determinant =0.

Of course, there are many methods, and there must be many that are faster than my calculations.