1 3* -1 Let A = В — -1 2 and C = 3 1 l1 2. 1. 1 -2. a.Use the above matrices to verify that (B + C)A = BA+ CA, if possible. Justify your answer in details. b. Use the above matrices to find A³, if possible. Justify your answer in details. c. Do you think it is possible to find a nonzero matrix, D, such that the matrix multiplication AD is possible and is equal to zero (AD = zero matrix)? If no, explain why in details? If yes, find such a matrix D. Justify your answer in details.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 29E
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Q1.
1
31
-1
41
B =
-1 2 andC =
Let A =
3
1
1.
1
-2]
a.Use the above matrices to verify that (B + C)A = BA + CA, if possible. Justify your answer in details.
b. Use the above matrices to find A³, if possible. Justify your answer in details.
c. Do you think it is possible to find a nonzero matrix, D, such that the matrix multiplication AD is
possible and is equal to zero (AD = zero matrix)? If no, explain why in details? If yes, find such a matrix
D. Justify your answer in details.
Transcribed Image Text:Q1. 1 31 -1 41 B = -1 2 andC = Let A = 3 1 1. 1 -2] a.Use the above matrices to verify that (B + C)A = BA + CA, if possible. Justify your answer in details. b. Use the above matrices to find A³, if possible. Justify your answer in details. c. Do you think it is possible to find a nonzero matrix, D, such that the matrix multiplication AD is possible and is equal to zero (AD = zero matrix)? If no, explain why in details? If yes, find such a matrix D. Justify your answer in details.
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