Determine whether the following subsets of R4 are vector subspaces. (a) V₁ = {(x, y, y, z)| x, y, ze R} (b) V = {(x, y, 0, 0)| x, y ≤ R} (c) Vc = {(x, y, 0, 1)| x, y ≤ R} (d) R¹ = {x =R¹| x; ≥0, Vi}

(a) No, V is not a subspace of R. The zero vector of R is (0, 0, 0, 0), but this vector is not in V. ...

Resuelto Determine whether the following subsets of R4 are

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Pregunta: Determine whether the following subsets of R4 are vector subspaces. (a) V₁ = {(x, y, y, z)| x, y, ze R} (b) V = {(x, y, 0, 0)| x, y ≤ R} (c) Vc = {(x, y, 0, 1)| x, y ≤ R} (d) R¹ = {x =R¹| x; ≥0, Vi}
Determine whether the following subsets of R4 are vector subspaces. (a) V₁ = {(x, y, y, z)| x, y, ze R} (b) V = {(x, y, 0, 0)| x, y ≤ R} (c) Vc = {(x, y, 0, 1)| x, y ≤ R} (d) R¹ = {x =R¹| x; ≥0, Vi}

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Solución
Paso 1

(a)
$\begin{aligned} V = {(x, y, y, z) ∣ x, y, z E R} \end{aligned}$
No, V is not a subspace of R.
Explanation:
The zero vector of R is (0, 0, 0, 0), but this vector is not in V. ...
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