For the matrix Z below, find the eigenvalues and eigenvectors. a. 1 0 -2 -2 0 4

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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For the matrix Z below, find the eigenvalues and eigenvectors.
a.
1 0 -2
Z = 0 5
(-2 0
4
b.
Verify if the function below is a linear transformation or not.
T:P: →R defined by T (a + bx + cx³) = [2a – b
-
i.
b+c]
ii.
L: R →R' defined by L = xy|
Given the following transformation L(u)=Au, where u = (x, y) and the standard (or induced)
с.
matrix A is given as A
i.
Sketch the triangle connecting the points (2, -2), (2, -5) and (5, -2). Then sketch its
transformation image if u represents the poit.
ii.
Identify the type of transformation shown above?
Transcribed Image Text:For the matrix Z below, find the eigenvalues and eigenvectors. a. 1 0 -2 Z = 0 5 (-2 0 4 b. Verify if the function below is a linear transformation or not. T:P: →R defined by T (a + bx + cx³) = [2a – b - i. b+c] ii. L: R →R' defined by L = xy| Given the following transformation L(u)=Au, where u = (x, y) and the standard (or induced) с. matrix A is given as A i. Sketch the triangle connecting the points (2, -2), (2, -5) and (5, -2). Then sketch its transformation image if u represents the poit. ii. Identify the type of transformation shown above?
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