suppose that u and v are both subspaces of r prove that u v u vue u an

Question

) Suppose that U and V are both subspaces of R". Prove that U + V = {u + v:ue U and v e V} is also a subspace of R". Es) Write down the subspace U + V explicitly if \mathrm{U}=\{(\mathrm{t},-3 \mathrm{t}, 5 \mathrm{t}): \mathrm{t} \in \mathrm{R}\} \text { and } \mathrm{V}=\{(0,7 \mathrm{t}, 2 \mathrm{t}): \mathrm{t} \in \mathrm{R}\} 5) Write down the subspace U + V explicitly if \mathrm{U}=\{(\mathrm{t}, 2 \mathrm{t}, 3 \mathrm{t}): \mathrm{t} \in \mathrm{R}\} \text { and } \mathrm{V}=\{(\mathrm{t},-2 \mathrm{t}, 0): \mathrm{t} \in \mathrm{R}\}