The vector b is in the subspace spanned by the columns of A when __ has a solution. The vector c is in the row space of A when __ has a solution. True or false: If the zero vector is in the row space, the rows are dependent.
The
The definition of row space and column space of a matrix is given as follows.
A column space of matrix is the space that is spanned by columns of
The row space of matrix is the space spanned by rows of .
We know that, Span.
Thus, if vector Span is equivalent to asking if there exists a vector such that
The vector is in the subspace spanned by the columns of when has a solution.
We know that column space of is equal to the row space of .
The vector is in the row space of when has a solution.
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