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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?

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?

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