Solve the systems of equations using matrices.4x+5y=83x-4y=3Leave answer in fraction form.4x+y+z=3-x+y=-11+2z2y+2z=-1-x

Let B be a 4x4 matrix to which we apply the following operations:
1. double column 1,
2. halve row 3,
3. add row 3 to row 1,
4. interchange columns 1 and 4,
5. subtract row 2 from each of the other rows,
6. replace column 4 by column 3,
7. delete column 1 (column dimension is reduced by 1).
(a) Write the result as a product of eight matrices.
(b) Write it again as a product of ABC (same B) of three matrices.

Find a basis for the space of $2\times 2$ diagonal matrices.
$\text{Basis }=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

simplify by combining like terms 4x-6x

Determine all $2\times 2$ matrices A such that AB = BA for any $2\times 2$ matrix B.

Find if possible the matrices:
a) AB
b) BA
$A=\left[\begin{array}{c}-1\\ -2\\ -3\end{array}\right],B=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$

Tell whether it’s matrices is in. Reduced form and the solution. If it’s not then give the row operation required to put it into reduced form
$\left[\begin{array}{ccccc}1& 0& -4& |& 0\\ 0& 1& 2& |& 0\\ 0& 0& 0& |& 1\end{array}\right]$

If T :${\mathbb{R}}^2\to {\mathbb{R}}^2$ is a linear transformation such that
$T\left(\left[\begin{array}{c}3\\ 6\end{array}\right]\right)=\left[\begin{array}{c}39\\ 33\end{array}\right]\text{ and }T\left(\left[\begin{array}{c}6\\ -5\end{array}\right]\right)=\left[\begin{array}{c}27\\ -53\end{array}\right]$
then the standard matrix of T is A