Consider the following. 9 10 A = 10 0 Find all eigenvalues λ of the matrix A. (Enter your answers as a comma-separated list.) λ = -1,10 Give bases for each of the corresponding eigenspaces. (Enter sqrt(n) for √n.) smaller A-value span 1 -sqrt(10) sqrt(10) larger λ-value span 1 Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ = D. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) (D, Q) = [[1,0],[0,10]], [[sq(1)" sqrt(1) sqrt( ]]

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 38EQ
Question

need help 5.4

Consider the following.
9
10
A =
10
0
Find all eigenvalues λ of the matrix A. (Enter your answers as a comma-separated list.)
λ = -1,10
Give bases for each of the corresponding eigenspaces. (Enter sqrt(n) for √n.)
smaller A-value span
1
-sqrt(10)
sqrt(10)
larger λ-value
span
1
Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ = D. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.)
(D, Q) =
[[1,0],[0,10]], [[sq(1)"
sqrt(1) sqrt(
]]
Transcribed Image Text:Consider the following. 9 10 A = 10 0 Find all eigenvalues λ of the matrix A. (Enter your answers as a comma-separated list.) λ = -1,10 Give bases for each of the corresponding eigenspaces. (Enter sqrt(n) for √n.) smaller A-value span 1 -sqrt(10) sqrt(10) larger λ-value span 1 Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ = D. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) (D, Q) = [[1,0],[0,10]], [[sq(1)" sqrt(1) sqrt( ]]
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