The discussion focuses on solving the matrix equation AB = BA, where Matrix A is defined as [[1, 1], [0, 1]] and Matrix B as [[a, b], [c, d]]. Participants calculated the resulting matrices from the multiplication and established that the elements of AB must equal those of BA, leading to four equations involving the variables a, b, c, and d. The next step involves solving these equations to find the specific coordinates for a, b, c, and d that satisfy the equation.
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Assuming your work so far is correct (I didn't check), set the elements of AB equal to those of BA. This will give you four equations in your four variables.leo255 said:Homework Statement
[/B]
Matrix A =
1 1
0 1
Matrix B =
a b
c d
Find coordinates on a, b, c, d such that AB = BA.
Homework Equations
The Attempt at a Solution
I calculated AB and BA with simple matrix multiplication, but am not sure where to go from here.
AB =
a + c a + b
c | d
BA =
a | a + b
c | c + d