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Question Number 183425 by ali009 last updated on 25/Dec/22

find the rank of the matrix A and B by   following row operation:  A= [(1,2,3,(−1)),((−2),(−1),(−3),(−1)),(1,0,1,(    1)),(0,1,1,(−1)) ]  B= [((    1),(    2),(−1),(     4)),((    2),(    4),(     3),(     5)),((−1),(−2),(     6),(−7)) ]

$${find}\:{the}\:{rank}\:{of}\:{the}\:{matrix}\:{A}\:{and}\:{B}\:{by} \\ $$$$\:{following}\:{row}\:{operation}: \\ $$$${A}=\begin{bmatrix}{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{−\mathrm{1}}\\{−\mathrm{2}}&{−\mathrm{1}}&{−\mathrm{3}}&{−\mathrm{1}}\\{\mathrm{1}}&{\mathrm{0}}&{\mathrm{1}}&{\:\:\:\:\mathrm{1}}\\{\mathrm{0}}&{\mathrm{1}}&{\mathrm{1}}&{−\mathrm{1}}\end{bmatrix} \\ $$$${B}=\begin{bmatrix}{\:\:\:\:\mathrm{1}}&{\:\:\:\:\mathrm{2}}&{−\mathrm{1}}&{\:\:\:\:\:\mathrm{4}}\\{\:\:\:\:\mathrm{2}}&{\:\:\:\:\mathrm{4}}&{\:\:\:\:\:\mathrm{3}}&{\:\:\:\:\:\mathrm{5}}\\{−\mathrm{1}}&{−\mathrm{2}}&{\:\:\:\:\:\mathrm{6}}&{−\mathrm{7}}\end{bmatrix} \\ $$

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