What is the Binomial Formula in Matrices without Evaluating Determinants?

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The discussion focuses on demonstrating a matrix equation involving two matrices without evaluating their determinants. The user expresses confusion about how to approach the problem, suspecting a connection to the binomial formula and scalar multiplication of matrices. A response suggests considering rules for column operations, which may simplify the task. The conversation highlights the challenge of solving the problem without determinant evaluation while seeking guidance on matrix manipulation techniques. Overall, the thread emphasizes the importance of understanding matrix operations in solving such equations.
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Homework Statement



I'm sorry this doesn't look too nice but it is supposed to be two matricces.

Show:

|1 a1-b1 a1+b1| |1 a1 b1|
|1 a2-b2 a2+b2|=2*|1 a2 b2|
|1 a3-b3 a3+b3| |1 a3 b3|

without evaluating the determinants.

Homework Equations



The Attempt at a Solution



It pretty obviously has got something to do with the 3. binomial formula and the rule that λ*A = λ*every value in the matrix.

I really don't know where to start on this, since I can't evaluate the determinants.
I'm pretty sure there is an easy way to do this, but I just can't see it.

Help is very much appreciated!

Thank you
 
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Hi Crution! Welcome to PF! :smile:

Do you know any rules for adding one column to another column? :wink:
 
thanks that was enough help :-)
 

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