Question

1. (a) Consider the set $X = \left\{ \begin{pmatrix} 1 \ 1 \ 1 \end{pmatrix}, \begin{pmatrix} 2 \ 0 \ -1 \end{pmatrix} \right\}$. (i) Find the Cartesian equation of Span(X). (ii) Find a basis of $\mathbb{R}^3$ that contains X. (b) Consider the set $V = \left\{ \begin{pmatrix} x \ y \ z \end{pmatrix} \in \mathbb{R}^3 \mid 3y + 2z = 5x \right\}$. Find a basis of V, and the dimension of V.

          1.
(a) Consider the set $X = \left\{ \begin{pmatrix} 1 \ 1 \ 1 \end{pmatrix}, \begin{pmatrix} 2 \ 0 \ -1 \end{pmatrix} \right\}$.
(i) Find the Cartesian equation of Span(X).
(ii) Find a basis of $\mathbb{R}^3$ that contains X.
(b) Consider the set $V = \left\{ \begin{pmatrix} x \ y \ z \end{pmatrix} \in \mathbb{R}^3 \mid 3y + 2z = 5x \right\}$. Find a basis of V, and the dimension of V.

$1. (a) Consider the set X = { < p m a t r i x > , < p m a t r i x > }. (i) Find the Cartesian equation of Span(X). (ii) Find a basis of ℝ^3 that contains X. (b) Consider the set V = { < p m a t r i x > ∈ℝ^3 | 3y + 2z = 5x }. Find a basis of V, and the dimension of V.$

Added by Albert B.

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