Question

[a] If \begin{Bmatrix} \begin{pmatrix} a \\ 1 \\ 1 \end{pmatrix}, \begin{pmatrix} 2 \\ a+1 \\ 2 \end{pmatrix}, \begin{pmatrix} 3 \\ 3 \\ a+2 \end{pmatrix} \end{Bmatrix} is linearly dependent in \(\mathbb{R}^3\), find a. [b] Find a basis for the solution space for AX = 0 where A = \begin{pmatrix} 1 & -1 & 2 & 3 \\ 2 & -3 & 1 & 2 \\ 3 & 2 & 1 & 4 \end{pmatrix}. What is the dimension for this solution space?

          [a] If \begin{Bmatrix} \begin{pmatrix} a \\ 1 \\ 1 \end{pmatrix}, \begin{pmatrix} 2 \\ a+1 \\ 2 \end{pmatrix}, \begin{pmatrix} 3 \\ 3 \\ a+2 \end{pmatrix} \end{Bmatrix} is linearly dependent in \(\mathbb{R}^3\), find a.

[b] Find a basis for the solution space for AX = 0 where A = \begin{pmatrix} 1 & -1 & 2 & 3 \\ 2 & -3 & 1 & 2 \\ 3 & 2 & 1 & 4 \end{pmatrix}. What is the dimension for this solution space?

[a] If
< p m a t r i x >
,
< p m a t r i x >
,
< p m a t r i x >
is linearly dependent in ℝ^3, find a.

[b] Find a basis for the solution space for AX = 0 where A =
< p m a t r i x >
. What is the dimension for this solution space?

Added by Ricardo A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert William Mead

08/16/2023

Step 1

Step 1: To determine if the vectors [a] and [b] are linearly dependent in IR³, we need to check if there exist scalars a and b such that a[b] = [a]. Show more…

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Texts: [a] If 3 is linearly dependent in IR³, find a +2 1 -1 2 3 2 -3 1 2 [b] Find a basis for the solution space for AX=O where A= What is the dimension for this 3 2 1 4 solution space?