Unimodular Matrix is a matrix, which has integer entries and determinant of &#x2208;<!-- ∈ -->

Assume that A is row equivalent to B. Find bases for Nul A and Col A.
$A=\left[\begin{array}{ccccc}1& 2& -5& 11& -3\\ 2& 4& -5& 15& 2\\ 1& 2& 0& 4& 5\\ 3& 6& -5& 19& -2\end{array}\right]$
$B=\left[\begin{array}{ccccc}1& 2& 0& 4& 5\\ 0& 0& 5& -7& 8\\ 0& 0& 0& 0& -9\\ 0& 0& 0& 0& 0\end{array}\right]$

Find an explicit description of Nul A by listing vectors that span the null space.
$A=\left[\begin{array}{ccccc}1& 5& -4& -3& 1\\ 0& 1& -2& 1& 0\\ 0& 0& 0& 0& 0\end{array}\right]$

Use the definition of Ax to write the matrix equation as a vector equation, or vice versa.
$\left[\begin{array}{cc}7& -3\\ 2& 1\\ 9& -6\\ -3& 2\end{array}\right]\left[\begin{array}{c}-2\\ -5\end{array}\right]=\left[\begin{array}{c}1\\ -9\\ 12\\ -4\end{array}\right]$

Find k$k$ such that the following matrix M$M$ is singular.

M=⎡⎣⎢−225+k−5933−4114⎤⎦⎥

What is the difference between solving an equation such as 5y + 3 - 4y - 8 = 6 + 9 and simplifying an algebraic expression such as 5y + 3 - 4y - 8 ? If there is a difference, which topic should be taught first ? Why ?