Consider the real vector spaces $R^4$ and $R^5$, and linear function:
$f: (a, b, c, d, e) ∈ R^5 → (a - d, a - d, e - d, c) ∈ R^4$.
• Find the kernel of $f$, its base and its dimension.
• Find the image of $f$, its base and its dimension.
My attempt to find the ker:
I made a system with $a - d, a - d, e - d, c$ and all the possible solutions are $(0,0,0,0,0)$, $(1,0,0,1,1)$, $(0,1,0,0,0)$, $(1,1,0,1,1)$...