Question

(b) Check to if S is a subspace of R?. If it is, find a basis and the dimension. \begin{equation} S = \left\{ \begin{bmatrix} x_1\\x_2\\x_3\\x_4 \end{bmatrix}, x_2 - x_3 + 2x_4 = 0 \right\} \subseteq \mathbb{R}^4 \end{equation}

          (b) Check to if S is a subspace of R?. If it is, find a basis and the dimension.
\begin{equation*}
S = \left\{ \begin{bmatrix} x_1\\x_2\\x_3\\x_4 \end{bmatrix}, x_2 - x_3 + 2x_4 = 0 \right\} \subseteq \mathbb{R}^4
\end{equation*}

$(b) Check to if S is a subspace of R?. If it is, find a basis and the dimension. S = { < b m a t r i x > , x2 - x3 + 2x4 = 0 }⊆ℝ^4$

Added by Amber V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Krishna G

Step 1

This means that the zero vector (0, 0, 0, 0) is in S. 2) S must be closed under addition: Let's take two vectors (T1, T2, T3, x4) and (T1', T2', T3', x4') in S. We need to show that their sum is also in S. (T1, T2, T3, x4) + (T1', T2', T3', x4') = (T1 + T1', T2 Show more…

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