Harvard University Find the Solutions For Continuity And Differentiability Math Ques

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Question 1
15 pts
Let e1, C2, … en be an orthonormal basis in R”. That means e; .e; = 1 for j =1,2,…n
and
@jºek = 0 for j #k
The vector product v1 X v2 in R3 is defined as determinant
ei
e2
e3
det
V11
V12
V13
V21
V22
U23
formally evaluated according to the Laplace rule with respect to the first row.
One can formally define the vector product vi X V2 X … X Un-1 in R” as determinant
ei
e2
en
V11
V12
Vin
det
Un-11
Un-12
Un-1n
formally evaluated according to the Laplace rule with respect to the first row.
Prove that
V1 V1
V1 V2
V1 · Un-1
V2 V1
V2.02
U2 · Un-1
|v1 X v2 X … X Un-112
= det
.
Un-101
Un-1 V2
Un-1 · Un-1
where n > 2 and lul2 = v • v for v ER.
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mathematical equations

Mathematical Values

Vector product

Compute the equations

Laplace rule

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