Let L: R$4$ R$3$ be defined by L$([$u$1$ u$2$ u$3$ u$4])=[$u$1$ u$2+$u$3$ u$3+$u$4]$

Let S$\text{'}=\{[1001],[0001],[1100],[0110]\}$ and T$\text{'}=\{[110],[010],[101]\}$

a$)$ Find a representation of L with respect to standard basis S and T for R$4$ and R$3.$

b$)$ Find the matrix L$\_$S$\text{'},$T$\text{'}$ with respect to S$\text{'}$ and T$\text{'}$

And can you explain all the steps and solutions