Level:
Project ID:
9000019904
Accepted:
1
Clonable:
0
Easy:
0
The coefficient matrix of a \(3\times 3\)
linear system is \(A\) and
the augmented matrix \(A'\).
Find \(\mathop{\mathrm{rank}}(A)\)
and \(\mathop{\mathrm{rank}}(A')\).
\[
A = \begin{pmatrix}
-1 & 3 & 2 \\
0 & 4 & -5 \\
0 & 0 & 2
\end{pmatrix} \qquad
A' = \left(\begin{array}{ccc|c}
-1 & 3 & 2 & 5 \\
0 & 4 & -5 & 10\\
0 & 0 & 2 & 0
\end{array}\right)
\]
\(\mathop{\mathrm{rank}}(A) = 3,\ \mathop{\mathrm{rank}}(A') = 3\)
\(\mathop{\mathrm{rank}}(A) = 2,\ \mathop{\mathrm{rank}}(A') = 3\)
\(\mathop{\mathrm{rank}}(A) = 3,\ \mathop{\mathrm{rank}}(A') = 2\)
\(\mathop{\mathrm{rank}}(A) = 2,\ \mathop{\mathrm{rank}}(A') = 2\)