# Thread: Help needed in matrices and solutions?

1. ## Help needed in matrices and solutions?

The augmented matrices of three systems of linear equation are given in row echelon form below.

(i)
|1 0 2 1|
|0 0 1 2|
|0 0 0 1|

(ii)
|1 0 2 1|
|0 1 −1 2|
|0 0 1 1|

(iii)
|1 0 2 1|
|0 0 1 2|
|0 0 0 0|

One of the systems has no solutions, one has one solution, and one has an infinite number of solutions. Identify which is which and solve the two that have solutions.

*give ur workings and a clear answer.

2. Originally Posted by federer
The augmented matrices of three systems of linear equation are given in row echelon form below.

(i)
|1 0 2 1|
|0 0 1 2|
|0 0 0 1|

(ii)
|1 0 2 1|
|0 1 −1 2|
|0 0 1 1|

(iii)
|1 0 2 1|
|0 0 1 2|
|0 0 0 0|

One of the systems has no solutions, one has one solution, and one has an infinite number of solutions. Identify which is which and solve the two that have solutions.

*give ur workings and a clear answer.
Well the first has no solutions as the last row corresponds to an equation:

$\displaystyle 0 \times x+0 \times y + 0 \times z=1$

Which has no solutions.

The last one has an ifinite number of solutions as there are only two effective equations, and they are linearly independednt.

The middle one has a unique solution and you show that by solving the system.

RonL