Question

6. For which values of a does \begin{equation} \text{span} \left\{ \begin{bmatrix} 1 \\ 0 \\ a \end{bmatrix}, \begin{bmatrix} 1 \\ 2 \\ -3 \end{bmatrix}, \begin{bmatrix} a \\ 1 \\ 0 \end{bmatrix} \right\} = \mathbb{R}^3? \end{equation}

          6. For which values of a does \begin{equation*} \text{span} \left\{ \begin{bmatrix} 1 \\ 0 \\ a \end{bmatrix}, \begin{bmatrix} 1 \\ 2 \\ -3 \end{bmatrix}, \begin{bmatrix} a \\ 1 \\ 0 \end{bmatrix} \right\} = \mathbb{R}^3? \end{equation*}

$6. For which values of a does span{ < b m a t r i x > , < b m a t r i x > , < b m a t r i x > } = ℝ^3?$

Added by David P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Joseph David

Step 1

In other words, we need to find values of a, b, and c such that for any vector (x, y, z) in R^3, there exist scalars s and t such that: (x, y, z) = s[H] + t[Y] + c[HE] Expanding this equation, we get: (x, y, z) = (s, 0, 0) + (0, t, 0) + (0, 0, c) From this Show more…

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