Linear Algebra

Linear Algebra: Vectors

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

Problem from group theory

in a group G, e is the identity .x,y belongs to G such that (x^5)(y^3)=(x^8)(y^5)=e. which one true a)x=e but y not = eb)x=y=ec)x not= e and y not= e

Choose a co-efficient that makes this system singular.

Choose a coefficient b that makes this system singular. Then choose a right side b that makes it solvable. Find two solutions in that singular case.
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Problem from group theory

in a group G, e is the identity .x,y belongs to G such that (x^5)(y^3)=(x^8)(y^5)=e. which one true a)x=e but y not = eb)x=y=ec)x not= e and y not= e

Choose a co-efficient that makes this system singular.

Choose a coefficient b that makes this system singular. Then choose a right side b that makes it solvable. Find two solutions in that singular case.
...

Linear Algebra: Vectors

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