Let ----0-- -2 = Show that {V₁, V2, V3} forms an orthogonal basis in R³. Express W= as a linear combination of v₁, V2 and v3. 2 -13 -11 3 =
Let ----0-- -2 = Show that {V₁, V2, V3} forms an orthogonal basis in R³. Express W= as a linear combination of v₁, V2 and v3. 2 -13 -11 3 =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Topic: Orthogonal Bases in Linear Algebra**
Let
\[
v_1 = \begin{bmatrix} 1 \\ -2 \\ 1 \end{bmatrix}, \quad v_2 = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix}, \quad v_3 = \begin{bmatrix} -5 \\ -2 \\ 1 \end{bmatrix}.
\]
Show that \(\{v_1, v_2, v_3\}\) forms an orthogonal basis in \(\mathbb{R}^3\). Express
\[
w = \begin{bmatrix} -13 \\ -11 \\ 3 \end{bmatrix}
\]
as a linear combination of \(v_1, v_2,\) and \(v_3\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbee182a-544b-4a35-ae8e-c9ecfc559983%2F6688718f-2f15-4b07-a5e6-788b362162c6%2F0g13g3pt_processed.png&w=3840&q=75)
Transcribed Image Text:**Topic: Orthogonal Bases in Linear Algebra**
Let
\[
v_1 = \begin{bmatrix} 1 \\ -2 \\ 1 \end{bmatrix}, \quad v_2 = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix}, \quad v_3 = \begin{bmatrix} -5 \\ -2 \\ 1 \end{bmatrix}.
\]
Show that \(\{v_1, v_2, v_3\}\) forms an orthogonal basis in \(\mathbb{R}^3\). Express
\[
w = \begin{bmatrix} -13 \\ -11 \\ 3 \end{bmatrix}
\]
as a linear combination of \(v_1, v_2,\) and \(v_3\).
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