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The rank of Matrix \(A =\left[ {\begin{array}{*{20}{c}} 1&0&0&0&1\\ 0&1&1&1&0\\ 0&1&1&1&0\\ 0&1&1&1&0\\ 1&0&0&0&1 \end{array}} \right]\) is _______.1. 22. 33. 44. 5 |
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Answer» Correct Answer - Option 1 : 2 \(A = \;\left[ {\begin{array}{*{20}{c}} 1&0&0&0&1\\ 0&1&1&1&0\\ 0&1&1&1&0\\ 0&1&1&1&0\\ 1&0&0&0&1 \end{array}} \right]\) \(\left| {\rm{A}} \right| = {\rm{\;}}\left| {\begin{array}{*{20}{c}} 1&0&0&0&1\\ 0&1&1&1&0\\ 0&1&1&1&0\\ 0&1&1&1&0\\ 1&0&0&0&1 \end{array}} \right|\) R5 → R5 – R1 R3 → R3 – R2 R4 → R4 – R2 \(\left| {\rm{A}} \right| = {\rm{\;}}\left| {\begin{array}{*{20}{c}} 1&0&0&0&1\\ 0&1&1&1&0\\ 0&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0 \end{array}} \right|\) Rank of the matrix is 2 |
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