Why Does exp(A+B) Not Equal exp(A)exp(B) for Certain Matrices?

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Can you please provide an example of 2x2 matrices A and B, where exp(A+B)\neqexp(A).exp(B)
 
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If A and B commute (i.e. AB=BA), then exp(A+B)=exp(A)exp(B). Can you find an example of two 2x2 matrices that don't commute?
 
Thread 'Have I solved this structural engineering equation correctly?'

Thread 'Have I solved this structural engineering equation correctly?'

Hi all, I have a structural engineering book from 1979. I am trying to follow it as best as I can. I have come to a formula that calculates the rotations in radians at the rigid joint that requires an iterative procedure. This equation comes in the form of: $$ x_i = \frac {Q_ih_i + Q_{i+1}h_{i+1}}{4K} + \frac {C}{K}x_{i-1} + \frac {C}{K}x_{i+1} $$ Where: ## Q ## is the horizontal storey shear ## h ## is the storey height ## K = (6G_i + C_i + C_{i+1}) ## ## G = \frac {I_g}{h} ## ## C...
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