Vector Sum

Construct the vector sum of this vector and another one.

Construct the vector sum of this vector and the other one.

Construct the vector sum of two vectors.

You could define sum vector right there.

Construct the vector sum starting at this point.

Select the point to construct the sum vector in...

I can say that vector x is going to be the sum, this is going to be the sum of this vector right here in green and this vector right here in red.

The sum of these two vectors is this vector right here.

My unit vector, let's just assume that u can be rewritten as my unit vector is equal to sum u1 and u2.

If you just sum these guys up in multiple combinations, you can get any vector up there.

So the position vector at any time can be written as a sum of its x and y components.

We know that any vector in Rn, let's say V2, can be represented as a sum of two vectors.

So in order for this to be closed under addition, a times vector 1 plus vector 2, the sum of these two vectors should also be a member of n.

So we could rewrite it vector 1, vector 2, vector 3, and vector 4.

Set of all of vectors that are x2 plus some scaled up sum of x0 minus x2. x0 minus x2 is this vector right here.

Vector a is equal to vector b plus vector a minus b.

If we're looking for the solution set to Ax is equal to 0, then that means is equal to the 0 vector, that that means that this sum, we're trying to find a solution set of this sum is equaling 0.

Well, it's this vector plus that vector.

I multiply this vector times this vector.

length of vector a minus vector b.

You know, for t as any real number, that's just a line, sum of the span of some unit vector. Where we assume this has length 1.

My first basis vector was the vector 2 minus 1 and my second basis vector is the vector 2, 1.

Sum

Sum

Sum

I'm going to multiply that vector times that row vector times this column vector.

And I did that because it has this neat property now because now the sum of two linear transformations operating on x is equivalent to, when you think of it is a matrix vector product, as the sum of their two matrices.

Let's find a vector that is orthogonal to these guys, and if I sum that vector to some linear combination of these guys, I'm going to get v3, and I'm going to call that vector y3. y3 is equal to v3 minus the projection of v3 onto the subspace spanned by u1 and u2.

Vector

vector

And vector c is the vector 7, 6.

Sorry, what is vector a plus vector b?

They're that basis vector times your vector x.

Let's call this vector, right here, vector b.

That means that our vector x is the 0 vector, and only the 0 vector.

So 1 times vector a plus 2 times vector b is equal to vector c.

So it's the span of vector 1, vector 2, all the way to vector n.

It's about zero sum and non zero sum games.

I could draw vector b. I could draw vector b over here. It's still vector b.

Times the vector, let me just call this vector x, that right there is vector x.

And then if you go from the tail of a all the way to the head of b all the way to the head b and you call that vector c and you call that vector c, that is the sum of a and b.

The sky vector may not be a null vector.

The direction vector may not be a null vector.

The right vector may not be a null vector.