Cet R3 be the set of all row vectors [x, y, z]. Which of the following sets constitute a subspace of R3? If not, then why? Illustrate each set, regard- ess if it is a subspace of R3 or not, with a picture. (a) All vectors of the form [0, y, z]. (b) All vectors of the form [1, y, z]. (c) All vectors of the form [x, 2x, 3x].

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. Let \(\mathbb{R}_3\) be the set of all row vectors \([x, y, z]\). Which of the following sets constitute a subspace of \(\mathbb{R}_3\)? If not, then why? Illustrate each set, regardless if it is a subspace of \(\mathbb{R}_3\) or not, with a picture.

(a) All vectors of the form \([0, y, z]\).

(b) All vectors of the form \([1, y, z]\).

(c) All vectors of the form \([x, 2x, 3x]\).
Transcribed Image Text:2. Let \(\mathbb{R}_3\) be the set of all row vectors \([x, y, z]\). Which of the following sets constitute a subspace of \(\mathbb{R}_3\)? If not, then why? Illustrate each set, regardless if it is a subspace of \(\mathbb{R}_3\) or not, with a picture. (a) All vectors of the form \([0, y, z]\). (b) All vectors of the form \([1, y, z]\). (c) All vectors of the form \([x, 2x, 3x]\).
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