The <row rank> of a <matrix> is the <dimension> of the <linear span> of its row vectors. Its <column rank> is the <dimension> of the <linear span> of its column vectors, equivalently the <dimension> of the <image> of the corresponding <linear map>. The <equality of row rank and column rank> states that \b[these two numbers are equal for every matrix]. Their common value is the <rank of a matrix>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / ib / Paper 3 / 10G / i / Solution

 Solution (source code)