Find the equation from the point (0, 0, 0) to the plane with equation 2x-y+3z=6.
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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solve #3 please, Show all of your work on pictures and explain each step you make.
Thank you!
![1. Find an orthogonal basis for the span of the set \( S \) in the vector space \( V \).
a. \(\{(6, -3, 2), (1, 1, 1), (1, -8, -1)\}\)
2. Find the distance from the point \((2, 3, 4)\) to the line in \(\mathbb{R}^3\) passing through \((0, 0, 0)\) and \((6, -1, -4)\).
3. Find the equation from the point \((0, 0, 0)\) to the plane with equation \(2x - y + 3z = 6\).
4. Suppose that a matrix \( A \) has the eigenvalues \(-3, 1\) (with algebraic multiplicity 2) and associated eigenvectors
\[
\begin{bmatrix}
1 \\
0 \\
2
\end{bmatrix},
\begin{bmatrix}
2 \\
-1 \\
2
\end{bmatrix},
\begin{bmatrix}
0 \\
-1 \\
0
\end{bmatrix}
\]
respectively. Write the diagonalization of \( A \) and find \( A \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0655393b-8df3-4633-b13c-e0d6983d2306%2F66a4ddfa-1945-48e4-8c20-fccfef76465a%2Fkfl16i9_processed.png&w=3840&q=75)
Transcribed Image Text:1. Find an orthogonal basis for the span of the set \( S \) in the vector space \( V \).
a. \(\{(6, -3, 2), (1, 1, 1), (1, -8, -1)\}\)
2. Find the distance from the point \((2, 3, 4)\) to the line in \(\mathbb{R}^3\) passing through \((0, 0, 0)\) and \((6, -1, -4)\).
3. Find the equation from the point \((0, 0, 0)\) to the plane with equation \(2x - y + 3z = 6\).
4. Suppose that a matrix \( A \) has the eigenvalues \(-3, 1\) (with algebraic multiplicity 2) and associated eigenvectors
\[
\begin{bmatrix}
1 \\
0 \\
2
\end{bmatrix},
\begin{bmatrix}
2 \\
-1 \\
2
\end{bmatrix},
\begin{bmatrix}
0 \\
-1 \\
0
\end{bmatrix}
\]
respectively. Write the diagonalization of \( A \) and find \( A \).
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