Multiple choice

The rank of the matrix$\begin{bmatrix} \ 1& 1& 1 \ \ 1 & -1 & 0 \ \ 1 & 1 & 1 \ \end{bmatrix}$is

  1. 0

  2. 1

  3. 2

  4. 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\text{We have} \\ A = \begin{bmatrix} \ 1 & 1 & 1 \ \ 1 & -1 & 0\ 1 & 1 &1 \ \end{bmatrix} \sim \begin{bmatrix} \ 1 & 1 & 1 \ \ 1 & -1 & 0\ 0 & 0 &0 \ \end{bmatrix} \hspace{2cm} R_3 - R_1 \\ \text{Since one full row is zero, $\rho(A) < 3$} \\ \text{Now} \begin{vmatrix} \ 1 & 1 \ \ 1 & -1 \ 0 & 0 \ \end{vmatrix} = 2 \neq 0, thus \hspace{0.2cm}\rho(A) = 2$

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