Question: Consider the vectors u1 = (1, 1, 1, 1), u2 = (0, 1, 1, 1), u3 = (0, 0, 1, 1) and u4 = (0, 0, 0, 1). Write down an arbitrary vector (a1, a2, a3, a4) ∈ ${R}^{4}$ as a linear combination of u1, u2, u3 and u4.

Can I just do $\left(\begin{array}{c}a1\\ a2\\ a3\\ a4\end{array}\right)=k\cdot u1\phantom{\rule{mediummathspace}{0ex}}+\phantom{\rule{mediummathspace}{0ex}}b\cdot u2\phantom{\rule{mediummathspace}{0ex}}+\phantom{\rule{mediummathspace}{0ex}}c\cdot u3+d\cdot u4$? Is that it? What is the question trying yo highlight with all those ones?

Can I just do $\left(\begin{array}{c}a1\\ a2\\ a3\\ a4\end{array}\right)=k\cdot u1\phantom{\rule{mediummathspace}{0ex}}+\phantom{\rule{mediummathspace}{0ex}}b\cdot u2\phantom{\rule{mediummathspace}{0ex}}+\phantom{\rule{mediummathspace}{0ex}}c\cdot u3+d\cdot u4$? Is that it? What is the question trying yo highlight with all those ones?