Linear Algebra: Vectors
Show that |a+b|^2 + |a-b|^2 = 2|a|^2 +|b|^2
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3 replies
Finguine_L
about 8 years ago
|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.
Benny_BB
about 8 years ago
Right hand side in equation is wrong. It is 2(|a|^2 +|b|^2).
Anita_fj
about 8 years ago
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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