First slide

Elementary row operations (Transformation)

Question

$The rank of [\begin{array}{ccc} 1 & 4 & - 1 \\ 2 & 3 & 0 \\ 0 & 1 & 2 \end{array}] is$

Moderate

A

0
B

1
C

2
D

3

Solution

$[\begin{matrix} 1 & 4 & - 1 \\ 2 & 3 & 0 \\ 0 & 1 & 2 \end{matrix}] \begin{matrix} R_{2} - 2 R_{1} \\ ~ \end{matrix} [\begin{matrix} 1 & 4 & 1 \\ 0 & - 5 & 2 \\ 0 & 1 & 2 \end{matrix}] \begin{matrix} 5 R_{3} + R_{2} \\ ~ \end{matrix} [\begin{matrix} 1 & 4 & 1 \\ 0 & - 5 & 2 \\ 0 & 0 & 12 \end{matrix}] ∴ R a n k = 3$

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