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Roldan

Calculus 3

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Let $W$ be the set of all vectors of the form $\left[\begin{array}{c}{s+3 t} \\ {s-t} \\ {2 s-t} \\ {4 t}\end{array}\right]$. Show that $W$ is a subspace of $\mathbb{R}^{4} .$ (Use the method of Exercise $11 . )$

Chapter 4

Vector Spaces

Section 1

Vector Spaces and Subspaces

in this video. I'm selling problem number 12 of section for my one. And, um basically, it asked us a show. It, uh, got said w is a subspace of are for, um, and said, w contains all the vectors in the form that fit this definition right here. I suppose three. T s minus two U two s minus t and for us for tea. Ah, as like the values of the vector. So if we set, don't you said w to be span UV? We know that, um, you as 11 to 0 because it's just the coefficients of the S terms in this definition, and V is three negative or negative one for because it's the coefficient off the tee terms in this definition that was given to us. So, um, we know that w must w set that spans u V with just means that it contains all the doctors in the in the form of UV added together like like this, given by the scientific definition. So to determine if probably use a subspace of, um, are for we have to make sure that it fits these three conditions. The definition of W W fits these conditions. One is that it must contain the zero vector. Um, and two is that it has to be closed under addition, And three is that it has to be closed in her skill in multiplication. Instead of trying to prove every single one of these, there is the easier way to solve this foam where theorem one just says that, um, someone from the section just says that if ve won t v p are in a better space V then span the one through three p is a subspace off the So here we find w span you envy already. And we know that you envy are in the set W because we're given this definition. So by theorem one w is a subspace love are for oh

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Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

06:36

In mathematics, a vector (from the Latin "mover") is a geometric object that has a magnitude (or length) and a direction. Vectors can be added to other vectors according to vector algebra, and can be multiplied by a scalar (real number). Vectors play an important role in physics, especially physics and astronomy, because the velocity and the momentum of an object are expressed by vectors.

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