A- [*] -2 -20 (a) Compute det(A). (b) Compute rank(A) and nullity(A). (c) Are the columns of A linearly independent? (d) Compute A-!. (e) Find the eigenvalues of A. (f) For each eigenvalue of A, find a corresponding eigenvector. (g) Find an invertible matrix P and a diagonal matrix D such that A = PDP-1. (h) Find all solutions to the equation 3 A

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 8E
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please slove a f g h

[
-2 -20
A =
7
(a) Compute det(A).
(b) Compute rank(A) and nullity(A).
(c) Are the columns of A linearly independent?
(d) Compute A-!.
(e) Find the eigenvalues of A.
(f) For each eigenvalue of A, find a corresponding eigenvector.
(g) Find an invertible matrix P and a diagonal matrix D such
that A = PDP-1.
(h) Find all solutions to the equation
3
A
=
2
Transcribed Image Text:[ -2 -20 A = 7 (a) Compute det(A). (b) Compute rank(A) and nullity(A). (c) Are the columns of A linearly independent? (d) Compute A-!. (e) Find the eigenvalues of A. (f) For each eigenvalue of A, find a corresponding eigenvector. (g) Find an invertible matrix P and a diagonal matrix D such that A = PDP-1. (h) Find all solutions to the equation 3 A = 2
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