Linear Systems and Vectors Quiz

Using the concept of vectors

The set of all vectors of size n

v = (v1, v2)

<p>By a diagonal arrow in a parallelogram</p> Signup and view all the answers

<p>Add and subtract</p> Signup and view all the answers

<p>Vector v generated by v1, ..., vp</p> Signup and view all the answers

<p>Collection of all possible linear combinations</p> Signup and view all the answers

<p>A solution set resulting from parametric vector equation</p> Signup and view all the answers

<p>As a question of linear combinations or expressed using vector equations</p> Signup and view all the answers

<p>{v1, v2, ..., vp} = x1v1 + x2v2 + ... + xpvp</p> Signup and view all the answers

<p>Take u and v in R^n, forming a plane</p> Signup and view all the answers

<p>The plane containing u, v, and the origin</p> Signup and view all the answers

<p>As a plane through the origin, whenever u and v are in R^n and v is not a multiple of u</p> Signup and view all the answers

<p>Span (u, v) = line through the origin containing u and v</p> Signup and view all the answers

<p>v, u, w ∈ R^n</p> Signup and view all the answers

<p>(u + v) = (v + u)</p> Signup and view all the answers

<p>u + (v + w) = (u + v) + w</p> Signup and view all the answers

<p>v + 0 = v</p> Signup and view all the answers

<p>There exists a vector -v such that v + (-v) = 0</p> Signup and view all the answers

<p>x(v + u) = xv + xu</p> Signup and view all the answers

<p>(x + y)v = xv + yv</p> Signup and view all the answers

<p>(xy)v = x(yv)</p> Signup and view all the answers

<p>|v| = v</p> Signup and view all the answers

<p>Take arbitrary vectors and compute their components: u + v = (u1 + v1, ..., Un + Vn) = (v1 + u1, ..., Vn + Un) = v + u</p> Signup and view all the answers