Matrices : Vector Equations

Please give step by step instructions and name each step like triangular form, augmented matrix etc so I know when and what to do and can understand it. We are not using calculator so the steps need to be shown to the solution. 1) Compute u + v and u - 2v u = -1 ; v = -3 2 -1 2) Display the following vector ...continues

Matrices Questions

Please give step by step solution in detail. Determine if b is a linear combination of the vectors formed from the columns of the matrix A. A = 1 -4 2 , b = 3 0 3 5 -7 -2 8 -4 -3 2) List 5 vectors in span (v1, v2). For each vector show the weights on v1 and v2 used to generate the vector and ...continues

Vector Subspaces

What would a vector v in R4 such that: V(1,2,1,0) T V(1,0,-1,1) T V(0,2,0,-1) = AND find scalars a,b,c,d such that <(1,2,1,0),(1,0,-1,1),(0,2,0,-1)> = Please note: denotes the vector subspace of Rn generated by the vectors v1,...,vk and that for scalars a1,...,an belonging to R, V(a1,...,an) = ...continues

Vector Subspaces

Suppose that V and W are vector subspaces of Rn. If I define: V + W = {v+w: v belonging to V, w belonging to W} How can I prove that V+W is also a vector subspace of Rn and ALSO how could verify that (for example) <(1,0,1), (-1,0,1)> + <(3,2,1)> = R3 Thanks

Vectors : Identities and Dot Products

How could you use the properties of the dot product to prove the following identities: (where u and v denote vectors in Rn) a) ||u + v||^2 + ||u-v||^2 = 2(||u||^2 + ||v||^2) b) ||u + v||^2 - ||u-v||^2 = 4u dot v Note: dot = dot product ^ = power ||= distance

vectors

Could you please give me some sort of a sketch or drawing of what a set S (its interior and its closure) would look like when: S= {(x,y) : -1<= y < cosx, -2# < x <= 2#} Note: <= is less than or equal to < is less than # is pi (3.14....)

vectors that are linearly independent

If the set{v1,v2,v3} of vectors in R^m is lineraly dependent, how do I know that the set {v1,v2,v3,v4} is also lineraly dependent for every choice of v4 in R^m?

Functions and graphs

Consider the functions (see attachment) and their graphs. (a) What is the largest domain, and corresponding range, of each function? (see attachment for rest of questions)

Functions and partial fractions

Show that just one of the functions (see attached file) is one-to-one on its largest domain.

Linear transformations

Consider the attached linear transformations of a plane with center O....See attached file