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Use row operations on [A | I] to find the inverse of A = 1, 1, 0; 1, 2, 1; 0, 1, 2…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Use row operations on $[A \,|\, I]$ to find the inverse of $A =

\displaystyle \begin{bmatrix} 1 & 1 & 0 \\ 1 & 2 & 1 \\ 0 & 1 & 2 \end{bmatrix}

$. Give the entries of$ A^{-1} $in row$ 1 $, column$ 1 $, in row$ 1 $, column$ 2 $, in row$ 2 $, column$ 2 $and in row$ 3 $, column$ 1$.

Need a reminder? The key ideaShow

Row operations on $[A \,|\, I]$ that reach $[I \,|\, A^{-1}]$ give the inverse. On an augmented matrix, a row $(0\ \dots\ 0 \,|\, c)$ with $c \ne 0$ means no solution. A junction gives the equation: flow in equals flow out.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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