linear algebra problem: How to show that this matrix is not invertable

[meow]

hi

my problem is stated in the uploaded picture.

 

[mmm4444bot]

Please check these results from googling keywords matrix not invertible.

 

[Deleted member 4993]

hi

my problem is stated in the uploaded picture.View attachment 1363

Now try R1 * -2 → R2

see what happens.

 

[pka]

hi

my problem is stated in the uploaded picture.View attachment 1363

Look at the determinate.
\(\displaystyle \left| {\begin{array}{*{20}c} 1 & 2 \\
2 & 1 \\


\end{array} } \right| - 2\left| {\begin{array}{*{20}c}
1 & 1 \\
2 & 1 \\


\end{array} } \right| + \left| {\begin{array}{*{20}c}
1 & 1 \\
1 & 2 \\


\end{array} } \right|
\)\(\displaystyle =-3+2+1=0\)
What does that tell you?