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a. {(6,-3,2), (1, 1, 1), (1, −8, −1)} 2. Find the distance from the point (2, 3, 4) to the line in R³ 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. Suppose that a matrix A has the eigenvalues -3 1 (with algebraic multiplicity 2) and associated 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 R³ 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. Suppose that a matrix A has the eigenvalues -3 1 (with algebraic multiplicity 2) and associated V

Advanced Engineering Mathematics
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 #2 please, Show all of your work on pictures and explain each step you make.

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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.**
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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