Anjurie

Linear Algebra: Vectors

Show that |a+b|^2 + |a-b|^2 = 2|a|^2 +|b|^2

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Finguine_L

|a-b|^2 will expand just like (a-b)^2. |a+b|^2 will provide two reulsts. one would be (a+b)^2 and would be -(a+b)^2. Adding these two will generate right side of equation.

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Benny_BB

Right hand side in equation is wrong. It is 2(|a|^2 +|b|^2).

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Anita_fj

In this simple linear algebra problem, take left side of equation

|a+b|^2 + |a-b|^2

|a+b|^2 = |a|^2 + |b|^2 + 2|a||b| either a>=b or a<b

|a-b|^2 = |a|^2 + |b|^2 - 2|a||b| either a>=b or a<b

Add these two and result is:

2(|a|^2+|b|^2) = Right hand side

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