Let M be a transformation matrix B &#x2192;<!-- \rightarrow --> B &#x2032; </m

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

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.
$A=\left[\begin{array}{c}-3\\ 2\\ 0\\ 1\end{array}\right]$

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

Find the inverse of the following matrix A, if possible. Check that $A{A}^{-1}=I$ and $A^{-1}A=I$
$A=\left[\begin{array}{cc}7& 4\\ 7& 7\end{array}\right]$
The inverse, $A^{-1}$ is ?

I have a hard time finding the analytical solution to the following non-linear equation:
$(1+x{)}^{1-p}+p^{\frac{p}{1-p}}x(p-1)-1=0$
where $p\in ]0,1[$ and $x>1$. I would like to have a solution $x$ in terms of $p$ for each fixed $p$ in the specified interval. Of course it's possible that no analytical form of the solution exists. If so, I'd also be happy to hear an argument why that is the case. However, for some values of p the solution is 'nice', for example for $p=\frac{1}{2}$ it's easy to compute that $x=8$ and for $p=\frac{1}{3}$ I obtained $x=\frac{9}{16}(5\sqrt{3}+\sqrt{11+64\sqrt{3}})$
Any kind of help is greatly appreciated!

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Tell whether the system has one solution, no solution, or infinitely many solutions. Write the solutions or, if there is no solution, say the system is inconsistent.

Which of the following statements are true/false?Justify your answer.
(i) ${\displaystyle R^2}$ has infinitely many non-zero, proper vector subspaces.
(ii) Every system of homogeneous linear equations has a non zero solution.