Solution Found!
Prove Theorem 2(b) and 2(c). Use the row–column rule. The
Chapter 2, Problem 29E(choose chapter or problem)
QUESTION:
Problem 29E
Prove Theorem 2(b) and 2(c). Use the row–column rule. The (I, j)-entry in A(B + C) can be written as
Theorem 2(b): A (B + C) = AB + AC
Theorem 2(c): (B + C)A = BA + CA
Questions & Answers
QUESTION:
Problem 29E
Prove Theorem 2(b) and 2(c). Use the row–column rule. The (I, j)-entry in A(B + C) can be written as
Theorem 2(b): A (B + C) = AB + AC
Theorem 2(c): (B + C)A = BA + CA
ANSWER:
Solution :
Step 1 :
Let A be an matrix and let B and C, have sizes for which the indicated . sum and product are defined.
The strategy of solution is to prove that
A ( B + C ) = AB + AC ,
And ( B + C )A = BA + CA.