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Exercise 5

Avg difficulty 3.0

Which of these subspaces of R3\mathbb{R}^{3}

W1W_{1}: the xx-axis, W2W_{2}: the yy-axis, W3W_{3}: the zz-axis,
W4W_{4}: the plane x+y+z=0x+y+z=0, W5W_{5}: the yzyz-plane

can be combined to

  • (a)  sum to R3\mathbb{R}^{3}?     (b)  direct sum to R3\mathbb{R}^{3}?

Hefferon, Linear Algebra, Vector Spaces, Combining Subspaces, Exercise 5

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.