Here are the steps to verify the given matrix properties:
Given matrices:
A=[3264],B=[−1178],C=[3149]
a) Verify (A+B)+C=A+(B+C)
Step 1: Calculate A+B.
A+B=[3264]+[−1178]=[3+(−1)2+16+74+8]=[231312]
Step 2: Calculate (A+B)+C.
(A+B)+C=[231312]+[3149]=[2+33+113+412+9]=[541721]
Step 3: Calculate B+C.
B+C=[−1178]+[3149]=[−1+31+17+48+9]=[221117]
Step 4: Calculate A+(B+C).
A+(B+C)=[3264]+[221117]=[3+22+26+114+17]=[541721]
Step 5: Compare the results.
Since [541721]=[541721], the statement (A+B)+C=A+(B+C) is verified.
Verified
b) Verify (A+B)−C=A+(B−C)
Step 1: Calculate A+B (from part a).
A+B=[231312]
Step 2: Calculate (A+B)−C.
(A+B)−C=[231312]−[3149]=[2−33−113−412−9]=[−1293]
Step 3: Calculate B−C.
B−C=[−1178]−[3149]=[−1−31−17−48−9]=[−403−1]
Step 4: Calculate A+(B−C).
A+(B−C)=[3264]+[−403−1]=[3+(−4)2+06+34+(−1)]=[−1293]
Step 5: Compare the results.
Since [−1293]=[−1293], the statement (A+B)−C=A+(B−C) is verified.
Verified
