Give an example of an (augmented) matrix in reduced row echelon form whose system of equations is inconsistent, and which does not have a pivot in every column.

Respuesta :

Answer:

[tex]\left[\begin{array}{ccc}4&0&3\\0&5&6\\0&0&2\end{array}\right][/tex]

Step-by-step explanation:

step 1 : you form a 3 x 3 matrix

step 2: you reduce the matrix to echelon form

step 3: you remove all pivot from the matrix

Step 4: you make sure that the system of equation is not solvable

The required augmented matrix

[tex]\begin{pmatrix} 1& 0& 0& 0 \\0 &1 &0 &0 \\ 0& 0& 0 &1 \\0 &0 & 0 &0 \\\end{pmatrix}[/tex]

Let us consider the augmented matrix,

[tex]\begin{pmatrix} 1& 0& 0& 0 \\0 &1 &0 &0 \\ 0& 0& 0 &1 \\0 &0 & 0 &0 \\\end{pmatrix}[/tex]

The above matrix is in the row reduced echelon form.

It has no pivot in the third column.

It is the system of the equation which is inconsistent as from the third row,

[tex]0 \times x_1+0 \times x_2+0 \times x_3=1\\0=1[/tex]

Which is not possible.

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