-91 Let y = -3 and u = and 2 orthogonal to u. x₁ = 4 -2 Write y as the sum of two orthogonal vectors, ₁ in Span {u} -3 , x₂ = =
-91 Let y = -3 and u = and 2 orthogonal to u. x₁ = 4 -2 Write y as the sum of two orthogonal vectors, ₁ in Span {u} -3 , x₂ = =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Vector Decomposition on an Educational Platform**
We are given the vectors:
\[
\mathbf{y} = \begin{bmatrix}
-9 \\
-3 \\
5 \\
\end{bmatrix}, \quad \mathbf{u} = \begin{bmatrix}
4 \\
-2 \\
-3 \\
\end{bmatrix}
\]
and we are asked to write \(\mathbf{y}\) as the sum of two orthogonal vectors, \(\mathbf{x}_1\) and \(\mathbf{x}_2\), where \(\mathbf{x}_1\) belongs to \(\text{Span} \{\mathbf{u}\}\) and \(\mathbf{x}_2\) is orthogonal to \(\mathbf{u}\).
This is represented mathematically as:
\[
\mathbf{x}_1 = \begin{bmatrix}
\text{input 1} \\
\text{input 2} \\
\text{input 3} \\
\end{bmatrix}, \quad \mathbf{x}_2 = \begin{bmatrix}
\text{input 4} \\
\text{input 5} \\
\text{input 6} \\
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30a42a85-c58f-45ac-a4af-faeed1a599e1%2F3215010e-9916-41e7-9b0f-77f872017ce2%2Fzsbbi2m_processed.png&w=3840&q=75)
Transcribed Image Text:**Vector Decomposition on an Educational Platform**
We are given the vectors:
\[
\mathbf{y} = \begin{bmatrix}
-9 \\
-3 \\
5 \\
\end{bmatrix}, \quad \mathbf{u} = \begin{bmatrix}
4 \\
-2 \\
-3 \\
\end{bmatrix}
\]
and we are asked to write \(\mathbf{y}\) as the sum of two orthogonal vectors, \(\mathbf{x}_1\) and \(\mathbf{x}_2\), where \(\mathbf{x}_1\) belongs to \(\text{Span} \{\mathbf{u}\}\) and \(\mathbf{x}_2\) is orthogonal to \(\mathbf{u}\).
This is represented mathematically as:
\[
\mathbf{x}_1 = \begin{bmatrix}
\text{input 1} \\
\text{input 2} \\
\text{input 3} \\
\end{bmatrix}, \quad \mathbf{x}_2 = \begin{bmatrix}
\text{input 4} \\
\text{input 5} \\
\text{input 6} \\
\end{bmatrix}
\]
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