4. Using the following matrices solve then verify the following properties:3 041 4 2^-6} --¹--:}A = −1 2B =C0 23 151 115 26 13D =+14-1 0 1 E = -1 1 23 2 44 13a. 2(D + E) = 2D + 2Eb. A(BC) = (AB)Cc. B-³ = (B-¹)³= (B−¹)³ = (B³)-1d. (D¹)−¹ = (D−¹)T

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4. Using the following matrices solve then verify the following properties: 3 0 4 A = --} -- 1 -- : } -1 2 B = 1 4 2 31 0 5 1 1 H 68 1 5 2 6 1 3 D= -1 0 1 E = -1 1 2 3 2 4 4 1 3 a. 2(D+E) = 2D + 2E b. A(BC) = (AB)C c. B−³ = (B−¹)³ = (B³)−¹ d. (D¹)−¹ = (D−¹)T

4. Using the following matrices solve then verify the following properties: 3 0 4 A = --} -- 1 -- : } -1 2 B = 1 4 2 31 0 5 1 1 H 68 1 5 2 6 1 3 D= -1 0 1 E = -1 1 2 3 2 4 4 1 3 a. 2(D+E) = 2D + 2E b. A(BC) = (AB)C c. B−³ = (B−¹)³ = (B³)−¹ d. (D¹)−¹ = (D−¹)T

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section: Chapter Questions

Problem 14RQ

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Question

4. Using the following matrices solve then verify the following properties:
3 0
4
1 4 2
^-6} --¹--:}
A = −1 2
B =
C
0 2
3 15
1 1
15 2
6 1
3
D =
+14
-1 0 1 E = -1 1 2
3 2 4
4 1
3
a. 2(D + E) = 2D + 2E
b. A(BC) = (AB)C
c. B-³ = (B-¹)³
= (B−¹)³ = (B³)-1
d. (D¹)−¹ = (D−¹)T

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