Exercise 3.4.5

Answers

Let $R$ be the matrix in reduced echelon form. We know that there is an invertible matrix $C$ such that $CA = R$ . This means

C (\begin{matrix} 1 & 0 & 1 \\ - 1 & - 1 & - 2 \\ 3 & 1 & 0 \end{matrix}) = I .

So we get

C^{- 1} = (\begin{matrix} 1 & 0 & 1 \\ - 1 & - 1 & - 2 \\ 3 & 1 & 0 \end{matrix}) .

And hence

A = C^{- 1} R = (\begin{matrix} 1 & 0 & 2 & 1 & 4 \\ - 1 & - 1 & 3 & - 2 & - 7 \\ 3 & 1 & 1 & 0 & - 9 \end{matrix}) .

jephianlin

2011-06-27 00:00