Linear Algebra
posted by Anthony
Hello, could anyone help me with this excersise of linear algebra, Please?
Well it's about linear transformation defined as T:VW , the excersices give me a set of linearly independent vectors of V {v1,v2, v3... vk} and then asks :
Are {W1, w2, w3, ...wk}, the linear transformation of v1, v2,.. , also linearly independent?
How can I demonstrate that?

Steve
google the topic. You will find many good discussions, such as this one:
http://math.stackexchange.com/questions/584132/proofoflinearindependenceofvectorsafterapplyingalineartransformation
Respond to this Question
Similar Questions

Linear Algebra
a)Let v be a fixed vector in R^3. Show that the transformation defined by T(u)=vxu is a linear transformation. b)Find the range of this linear transformation. Thanx 
algebra
If v1,...,v4 are in R^4 and v3 is not a linear combination of v1, v2, v4 then {v1, v2, v3, v4] is linearly independent. Is this true or false? 
Math: Linear Algebra
Let T1: P1 > P2 be the linear transformation defined by: T1(c0 + c1*x) = 2c0  3c1*x Using the standard bases, B = {1, x} and B' = {1, x, x^2}, what is the transformation matrix [T1]B',B T(c0 + c1*x) = 2c0  3c1*x > T(1) … 
Algebra
Determine if the relationship represented in the table is linear. If it is linear, write an equation. x 2 5 7 10 12 20 y 3 0 2 5 7 15 A) Linear; y = x  5 B) Linear; y = 5x C) Linear; y = x + 5 D) Not linear I'm thinking it's C … 
Linear Algebra
(1) Define T:R>R be a linear transformation such that T(x,y,z)= (2x,2y,2z) then the given value of T is A. 3 B. 2 C. 4 D. 6 (A) (B) (C) (D) (2) Let V and W be vector spaces over a field F, and let T:V> W be a linear transformation … 
Linear algebra
Find two vectors v and w such that the three vectors u = (1,1,1), v and w are linearly independent independent. 
Linear Algebra
Prove that If a vector space is of dimension n and a set of vectors spans V, then that set of vectors must be linearly independent. 
linear algebra
Solve using the concept of rank. Is S={−16 −7 −21,2 1 3, 21 9 2} a linearly independent set of vectors in R3? 
Ross
Hello, can anyone give me some help with these excersises? 
linear algebra
Hello, how can I proof the next theorem? I have a linear transformation T(X) that can be express as T(X)=AX and A is an orthogonal matrix, then T (X)=X , I was doing this: T (X)=sqrt(<AX,AX>) But I don't know what