There are more answers to this problem, but I'm not sure how to approach it. The subspaces of [tex]R^3[/tex] are planes, lines, [tex]R^3[/tex] itself, or Z containing only (0,0,0,0). b. Describe the five type of subspaces of [tex]R^4[/tex] i. lines thru (0,0,0,0) ii. zero (0,0,0,0) iii. planes thru (0,0,0,0) What do you mean by planes? Are you assuming 2 dimensional sets as is usual with planes? iv. itself, [tex]R^4[/tex] What's the 5th?