First slide

Elementary row operations (Transformation)

Question

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

Easy

A

0
B

1
C

2
D

3

Solution

$[\begin{matrix} 1 & 2 & - 1 \\ 4 & 1 & 2 \\ 3 & - 1 & 1 \\ 1 & 2 & 0 \end{matrix}] R_{2} \to R_{2} - 4 R_{1}, R_{3} \to R_{3} - 3 R_{1}, R_{4} \to R_{4} - 4 R_{1} [\begin{matrix} 1 & 2 & - 1 \\ 0 & - 7 & 6 \\ 0 & - 7 & 4 \\ 0 & 0 & 1 \end{matrix}] H e n c e r a n k o f t h e m a t r i x i s 3$

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