LA2.2.6

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A={\begin{bmatrix}1&5&4\\0&3&2\\2&13&10\end{bmatrix}}\,

R_{3}-2R_{1}={\begin{bmatrix}1&5&4\\0&3&2\\0&3&2\end{bmatrix}}\,

R_{2}-R_{3}={\begin{bmatrix}1&5&4\\0&3&2\\0&0&0\end{bmatrix}}\,

Rank of A is 2 since the number of non-zero rows is 2.

Now,B={\begin{bmatrix}1&1&1\\2&2&2\\3&3&3\end{bmatrix}}\,

R_{2}-2R_{1},R_{3}-3R_{1}={\begin{bmatrix}1&1&1\\0&0&0\\0&0&0\end{bmatrix}}\,

Therefore,Rank of B is 1.

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