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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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
Transcribed Image Text: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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