Find a 3×33×3 matrix AA such that Ax⃗ =9x⃗ Ax→=9x→ for all x⃗ x→ in R 

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

For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A.
$A=\left[\begin{array}{cccc}2& 3& 5& -9\\ -8& -9& -11& 21\\ 4& -3& -17& 27\end{array}\right]$
Find a nonzero vector in Nul A.
$A=\left[\begin{array}{c}-3\\ 2\\ 0\\ 1\end{array}\right]$

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 matrix of linear transformation
A linear transformation
${\displaystyle T:{\mathbb{R}}^2\to {\mathbb{R}}^2}$
is given by
${\displaystyle T\left(i\right)=i+j}$
${\displaystyle T\left(j\right)=2i-j}$

I have a 3d object, to which I sequentially apply 3 ${\displaystyle 4\times 4}$ transformation matrices, A, B, and C. To generalize, each transformation matrix is determined by the multiplication of a rotation matrix by a translation matrix.
How can I calculate the final transformation matrix t, which defines how to get from the original 3d object to the final transformed object?

Do elementary row operations give a similar matrix transformation?
So we define two matrices A, B to be similar if there exists an invertible square matrix P such that ${\displaystyle AP=PB}$.

Write the system first as a vector equation and then as a matrix equation.
${\displaystyle 8x_1-x_2=4}$
${\displaystyle 5x_1+4x_2=1}$
${\displaystyle x_1-3x_2=2}$