Question

Let \begin{pmatrix} 2 \\ 0 \\ 1 \end{pmatrix} u = \begin{pmatrix} 1 \\ 3 \\ 2 \end{pmatrix} , and w = \begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix} (1) Calculate the norm of each vector. (3 points) (2) Are these vectors pairwise orthogonal? (3 points) (3) Are these vectors independent? (4 points) (4) Can they constitute a base for $\mathbb{R}^3$ ? Explain. (3 points)

          Let
\begin{pmatrix} 2 \\ 0 \\ 1 \end{pmatrix}
u = \begin{pmatrix} 1 \\ 3 \\ 2 \end{pmatrix}
, and
w = \begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix}
(1) Calculate the norm of each vector. (3 points)
(2) Are these vectors pairwise orthogonal? (3 points)
(3) Are these vectors independent? (4 points)
(4) Can they constitute a base for
$\mathbb{R}^3$
? Explain. (3 points)

Let

< p m a t r i x >

u =
< p m a t r i x >

, and
w =
< p m a t r i x >

(1) Calculate the norm of each vector. (3 points)
(2) Are these vectors pairwise orthogonal? (3 points)
(3) Are these vectors independent? (4 points)
(4) Can they constitute a base for
ℝ^3
? Explain. (3 points)

Added by Michelle S.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Justin Swantek

Step 1

In this case, we have two vectors: -G and ~~0. Since -G is a scalar multiple of the vector G, we can say that the norm of -G is equal to the norm of G, which is denoted as ||G||. The norm of ~~0 is equal to the norm of 0, which is 0. Show more…

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Let "-G ~0 and ~~0 (1) Calculate the norm of each vector: (3 points) Are these vectors pairwise orthogonal? (3 points) Are these vectors independent? (4 points) 4) Can they constitute a base for Explain: (3 points)