Assignment 6: Problem 16
(1 point)
Results for this submission
2 of the questions remain unanswered.
Group the statements below into two sets of equivalent statements. That is, given any specific $n \times n$ matrix $A$ (where $n \ge 2$), all the statements in one group will be true and all the statements in the other group will be false. (Which group is true and which is false depends of course on $A$).
1. There exists an $n \times n$ matrix $B$ such that $AB = I = BA$.
2. The homogeneous system $Ax = 0$ has infinitely many solutions.
3. There exist elementary matrices $E_1, E_2, \dots, E_k$ such that $E_1 E_2 \dots E_k A = 4I$.
4. For every vector $b \in \mathbb{R}^n$, the linear system $Ax = b$ has a unique solution.
5. There exist distinct vectors $u, v \in \mathbb{R}^n$ such that $Au = 0$ and $Av = 0$.
6. The rank of $A$ is less than $n$.
7. The reduced row echelon form of $A$ is the identity matrix.
8. $\det(A) = 0$
Write each set as numbers separated by commas, in increasing order.
Frist group: Second group:
