Question

Let $A$ be a $3 \times 5$ matrix defined by
$A = \begin{pmatrix}0 & 1 & 3 & 1 & 2 \\\1 & 6 & 2 & 3 & 4 \\\1 & 8 & 8 & 5 & 8\end{pmatrix}.$
Consider the system of linear equations given by
$A \begin{pmatrix}x_1 \\\x_2 \\\x_3 \\\x_4 \\\x_5\end{pmatrix} = \begin{pmatrix}3 \\\1 \\\10\end{pmatrix},$
where $x_1, x_2, x_3, x_4, x_5$ are real variables. Then

• A. the rank of 𝐴 is 2 and the given system has a solution
• B. the rank of 𝐴 is 2 and the given system does NOT have a solution
• C. the rank of 𝐴 is 3 and the given system has a solution
• D. the rank of 𝐴 is 3 and the given system does NOT have a solution

Answer 1

Answer: (B)

the rank of 𝐴 is 2 and the given system does NOT have a solution

Answer 2

The correct option is (B): the rank of 𝐴 is 2 and the given system does NOT have a solution