snowlovelydayM

2021-01-13

Let

and let

Convince me that D is a subspace of

Dora

Skilled2021-01-14Added 98 answers

We will denote the scalar product as

Let

Then

This is because, since v, w in D, we have that

So,

Similarly, we get that

Thus,

This proves that D is a subspace of

. Now let

Then we have that

Thus, we have a system of equations

The matrix of this homogeneous system is

We will now use the following elementary row operations:

1. Interchange the ith and jth row:

. 2, Multiply the eth row by a constant

3. Multiply the jth row by a constant c and add it to the ith row:

This means that we have to have 2 parameters:

This means that

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