1. For a matrix \( A \) with \( m \) rows and \( n \) columns such that \( m<n \), the nullspace has a larger dimension than? (Pick only one of a to \( d \) which is the right answer). Explain your answer. (a) \( n-r \) (b) \( m-r \) (c) \( \mathrm{m} \) (d) \( \mathrm{n} \)
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The dimension of the nullspace is the number of free variables in the system of equations represented by the matrix, which is also the number of columns of the matrix minus the rank of the matrix (the maximum number of linearly independent columns). Given that \( Show more…
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