How many solutions does the following system have? Enter 1 if there is only one solution, 0 if there are no solutions and -1 if there are infinitely many solutions. The coefficient matrix 𝐴A and the vector 𝑏b are given below:𝐴=[10−111−121−2],𝑏=[134]A= ​ 112​ 011​ −1−1−2​ ​ ,b= ​ 134​ ​

To determine the number of solutions for the system of equations, we first need to form the augmented matrix [A|b]. The augmented matrix is:

[10 -1 | 1]
[11 -1 | 3]
[1 -2 | 4]

Next, we perform Gaussian elimination or Gauss-Jordan elimination to bring the matrix to row-echelon form or reduced row-echelon form.

Subtract the first row from the second row and the first row from the third row:

[10 -1 | 1]
[ 1  0 | 2]
[-9 -1 | 3]

Next, multiply the first row by 9 and add it to the third row:

[10 -1 | 1]
[ 1  0 | 2]
[ 0 -10| 12]

Finally, divide the third row by -10:

[10 -1 | 1]
[ 1  0 | 2]
[ 0  1 | -1.2]

The system of equations now corresponds to:

10x - y = 1
x = 2
y = -1.2

Substitute x = 2 into the first equation:

10*2 - y = 1
20 - y = 1
y = 19

But from the third equation, we have y = -1.2. This is a contradiction, so the system of equations has no solution. Therefore, the answer is 0.