Verify the parallelogram law for vectors u and v in

berljivx8 2021-12-17 Answered

Verify the parallelogram law for vectors u and v in Rn:∥u+v2+uv2=2u2+2v2

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Expert Answer

alexandrebaud43
Answered 2021-12-18 Author has 36 answers

u+v2+uv2
=(u+v)(u+v)+(uv)(uv)
=(uu+vu+uv+vv)+(uuvuuv+vv)
=2uu+2vv
=2u2+2v2
Hint:
u2=uu

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enlacamig
Answered 2021-12-19 Author has 30 answers

Let u,vRn. Then we have
u+v2=(u+v)(u+v)
=∥u2+2(uv)+v2
Also,
uv2=(uv)(uv)
=∥u22(uv)+v2
Therefore,
u+v2+uv2=∥u2+2(uv)+v2+u22(uv)+v2
2u2+2v2

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