Consider the 3 !!! 5 matrix A = ? 3 -6 -8 -8 5 ? ? -6 12 3 3 3 ? ? -4 8 0 0 4 ?, which can be row reduced to the following matrix: ? 1 -2 0 0 -1 ? ? 0 0 1 1 -1 ? ? 0 0 0 0 0 ?. The rank of A is . The nullity of A is . For a 3 !!! 5 matrix, the rank plus the nullity is always equal to .
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The rank of a matrix is the number of linearly independent rows or columns in the matrix. After row reduction, the matrix becomes: \[ \begin{pmatrix} 1 & -2 & 0 & 0 & -1 \\ 0 & 0 & 1 & 1 & -1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix} \] In this reduced matrix, there Show more…
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