1.(a) If A is invertible and AB = AC, prove that B = C.
(b) Let A =24
1 135 explain why A is not invertible.
(c) Let A =24
1 135, ¯nd 2 matrices B and C, B 6= C such that AB = AC.
(a) If a square matrix A has the property that row 1 + row 2 = row 3, clearly explain why
the matrix A is not invertible.
(b) If any square matrix B has the property that one row equals the sum of multiples of
the other rows, clearly explain why the matrix B is not invertible.
In class, we will show (Section 3.5) that AB is an invertible matrix if and only if A
See attached file for full problem description. #1 and 2 only.
The final answers are:
A is not invertible. Why? For step by ...
Solutions to the posted problems are given with step by step explanation in such a way that the students understand the procedure and method involved in solving such type of problems and also could use these solutions as model solutions to solve other similar problems using these solutions.