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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)}

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)}

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 #1 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 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. 4. Suppose that a matrix A has the eigenvalues -3, 1 (with algebraic multiplicity 2) and associated 2 0 HAH eigenvectors 0 -1 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 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. 4. Suppose that a matrix A has the eigenvalues -3, 1 (with algebraic multiplicity 2) and associated 2 0 HAH eigenvectors 0 -1 respectively. Write the diagonalization of A and find A.
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