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Mathematics - Matrices - Invertible Matrices

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1.(a) If A is invertible and AB = AC, prove that B = C.
(b) Let A =24
1 1
1 135 explain why A is not invertible.
(c) Let A =24
1 1
1 135, ¯nd 2 matrices B and C, B 6= C such that AB = AC.

2.
(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.

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