Exercise 3.2.3

Question

By further row operations on each $U$ in Problem 1, find the reduced echelon form $R$. True or false with a reason: The nullspace of $R$ equals the nullspace of $U$.

Prakash Anand · Accepted Answer

$$R=\left[\begin{array}{lllll}1 & 2 & 0 & 0 & 0 \ 0 & 0 & 1 & 2 & 3 \ 0 & 0 & 0 & 0 & 0\end{array}ight],\quad R=\left[\begin{array}{ccc}1 & 0 & -1 \ 0 & 1 & 1 \ 0 & 0 & 0\end{array}ight],$$

$R$ has the same nullspace as $U$ and $A$.

Exercise 3.2.3

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Exercise 3.2.3

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