Row Space
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In linear algebra, the row space of a matrix is the set of all possible linear combinations of its row vectors. The row space of an m × n matrix is a subspace of n-dimensional Euclidean space. The dimension of the row space is called the rank of the matrix. Let A be an m × n matrix, with row vectors r1, r2, ..., rm. A linear combination of these vectors is any vector of the form c_1 textbf{r}_1 + c_2 textbf{r}_2 + cdots + c_m textbf{r}_mtext{,} where c1, c2, ..., cm...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In linear algebra, the row space of a matrix is the set of all possible linear combinations of its row vectors. The row space of an m × n matrix is a subspace of n-dimensional Euclidean space. The dimension of the row space is called the rank of the matrix. Let A be an m × n matrix, with row vectors r1, r2, ..., rm. A linear combination of these vectors is any vector of the form c_1 textbf{r}_1 + c_2 textbf{r}_2 + cdots + c_m textbf{r}_mtext{,} where c1, c2, ..., cm are constants. The set of all possible linear combinations of r1,...,rm is called the row space of A. That is, the row space of A is the span of the vectors r1,...,rm. The dimension of the row space is called the rank of the matrix. This is the same as the maximum number of linearly independent rows that can be chosen from the matrix. For example, the 3 × 3 matrix in the example above has rank two. The rank of a matrix is also equal to the dimension of the column space.
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