2a*|2a.. 1..|

.....|a^2..2a|-

|a^2... 1..|

|0....2a..|

When = 6a 3-2a 3 = 4a 3 ≠ 0, that is, a≠0, the system of equations has a unique solution.

Perform row transformation on the expansion matrix:

2a... 1...0.... 1

a^2..2a. 1...0

0..a/2... 1....0

(omit matrix symbols),

Subtract the third line from the second line, and then divide it by 3a/2 to get

2a... 1...0.... 1

2a/3. 1..0....0

0...a/2.. 1....0

Subtract the second line from the first line and divide it by 4a/3.

1....0....0....3/(4a)

2a/3. 1..0....0

0...a/2.. 1....0

Subtract 2a/3 times of the first row from the second row,

1....0....0....3/(4a)

0.... 1....0...- 1/2

0...a/2.. 1....0

Subtract a/2 times of the second line from the third line.

1....0....0....3/(4a)

0.... 1....0...- 1/2

0....0.... 1...a/4。

∴x=(x 1，x2，x3)^T

=(3/(4a),- 1/2,a/4)^T.