Problem 7. Determine whether the set S is subspace of R³ defined by S = {(₁, 72, 7, ₁, ₁) R: ₁3₂ and 3=77₁). [10 marks]

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Problem 7 Determine Whether The Set S Is Subspace Of R Defined By S 72 7 R 3 And 3 77 10 Marks 1 (14.25 KiB) Viewed 15 times

Problem 7. Determine whether the set S is subspace of R³ defined by S = {(₁, 72, 7, ₁, ₁) R: ₁3₂ and 3=77₁). [10 marks] Problem 8. Suppose U=((r.y.z+y.z-y. 2r) F³ :z,y € F). Find a subspace W of F such that F-U@W. [10 marks] Problem 9. Let S be a subset of F" defined as S= {(r,y,z) Fr+y+2:-1=0}. Then determine S is a subspace of F¹ or not. [10 marks] Problem 10. Suppose U is a subspace of V. Then show that U+U=U. [10 marks]