a) Factor the matrix A into the product XDX-1 where D is diagonal.(-1-22A =43-4-2b) Verify that A = XDX-1 and discuss why A is diagonalizable.c) Use part (a) to find A³ and A-1.wu loin 16:0 lutatoll, nõil paa|ulalolaiolnil lia ulaloll yilolg uw gihimiLet T he a mannina from R4 into R3 defined hvull li.claw

Answered: Image /qna-images/answer/5b0d00ff-bbda-4fa6-8d17-7c8e5c30725c.jpg

Answered: a) Factor the matrix A into the product…

a) Factor the matrix A into the product XDX- where D is diagonal. (-1 -2 2 A = 4 3 -4 -2 b) Verify that A = XDX-1 and discuss why A is diagonalizable. %3D c) Use part (a) to find A³ and A-1.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.9: Properties Of Determinants

Problem 46E

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

100%

a) Factor the matrix A into the product XDX-1 where D is diagonal.
(-1
-2
2
A =
4
3
-4
-2
b) Verify that A = XDX-1 and discuss why A is diagonalizable.
c) Use part (a) to find A³ and A-1.
wu loin 16:0 lutatoll, nõil paa|
ulalo
laiolnil lia ulaloll yilolg uw gihimi
Let T he a mannina from R4 into R3 defined hv
ull li
.claw

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