A plane α is given via the equationα : x + 2y − z − 2 = 0 .The line l passes through the points A = (1, 2, −1) and B = (2, 3, 0).(a). Find the coordinates of the point of intersection of the line l and theplane α. (b). Find the distance from the point A to the plane α. (a). Find a 2 × 2 matrix A such that (-4,0) and (-2, –4) are eigenvectorsof A corresponding eigenvalues 9 and –7.-(b). Let B be the matrix( )3 24 1Find the eigenvalues and corresponding eigenvectors of B.(c). Find the eigenvalue of C corresponding to the eigenvector (–1, 1,0)*(t stands for transposition) given that C is the matrix105--9 - 4 9554-

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A plane α is given via the equation α : x + 2y − z − 2 = 0 . The line l passes through the points A = (1, 2, −1) and B = (2, 3, 0). (a). Find the coordinates of the point of intersection of the line l and the plane α. (b). Find the distance from the point A to the plane α.

A plane α is given via the equation α : x + 2y − z − 2 = 0 . The line l passes through the points A = (1, 2, −1) and B = (2, 3, 0). (a). Find the coordinates of the point of intersection of the line l and the plane α. (b). Find the distance from the point A to the plane α.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices

Problem 24EQ

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Question

A plane α is given via the equation
α : x + 2y − z − 2 = 0 .
The line l passes through the points A = (1, 2, −1) and B = (2, 3, 0).

(a). Find the coordinates of the point of intersection of the line l and the
plane α.

(b). Find the distance from the point A to the plane α.

(a). Find a 2 × 2 matrix A such that (-4,0) and (-2, –4) are eigenvectors
of A corresponding eigenvalues 9 and –7.
-
(b). Let B be the matrix
( )
3 2
4 1
Find the eigenvalues and corresponding eigenvectors of B.
(c). Find the eigenvalue of C corresponding to the eigenvector (–1, 1,0)*
(t stands for transposition) given that C is the matrix
10
5
-
-9 - 4 9
5
5
4
-

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