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Engineering Mathematics

Row Echelon Form

The rank of t...

Question

The rank of the matrix $⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 1 & 4 & 8 & 7 0 & 0 & 3 & 0 4 & 2 & 3 & 1 3 & 12 & 24 & 2 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦$

A

3

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B

1

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C

2

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D

4

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Solution

The correct option is D 4
Given $A = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 1 & 4 & 8 & 7 0 & 0 & 3 & 0 4 & 2 & 3 & 1 3 & 12 & 24 & 2 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦$

$R_{2} \leftrightarrow R_{3}$
$R_{2} \to R_{2} - 4 R_{1}$
$R_{4} \to R_{4} - 3 R_{1}$

$A \sim ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 1 & 4 & 8 & 7 0 & - 14 & - 29 & - 27 0 & 0 & 3 & 0 0 & 0 & 0 & - 19 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦$

= Echelon form
Number of non-zero rows is 4

So $ρ (A) = 4$

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