Math  Algebraic Vectors
posted by Anonymous .
Given the vectors:
u = [3, 0]
v = [1, 2]
a) Express the vector w = [2, 8] as a linear combination of vectors u and v.
How do I do this?

Math  Algebraic Vectors 
Reiny
let [2,8] = a[3,0] + b[1,2]
so you get 3a  b = 2
and 2b = 8
from the second equation b = 4, subbing that back in to the first...
3a  4 = 2
a = 2
check to see if [2,8] = 2[3,0] + 4[1,2]
sure does!
We were lucky that in the second equation one of the variables dropped out, normally you would end up solving 2 equations in 2 unknowns. 
Math  Algebraic Vectors 
Anonymous
What? I don't understand what you did. . .
Respond to this Question
Similar Questions

math
If A^TA is an invertible matrix, prove that the column vectors of A are linearly independent. You know that if statement X implies statement Y then that is equivalent to Not(Y) implies Not(X). You can start by taking the column vectors … 
physics [vectors]
The concept i get, but somehow i just can't execute this problem, please help me! You are given vectors A = 5.5 6.2 and B =  3.7 7.4 . A third vector C lies in the xyplane. Vector C is perpendicular to vector A and the scalar product … 
12th grade
prove that normal to plane containing 3 points whose position vectors are a vector,b vector,c vectorlies in direction addition of cross product of vectors b and c and cross product of vectors c and a and cross product of vectors a … 
Calculus
Name two sets of vectors that could be used to span a set in R^3. Show how the vectors (1,2,0) and (3,4,0) could each be written as a linear combination of the vectors you have chosen. 
Mamthematics  Vectors
a) If vector u and vector v are noncollinear vectors show that vector u, vector u cross product vector v and (vector u cross product vector v) cross product vector u are mutually othogonal. b) Verify this property using vectors collinear … 
maths
Given that vector c and vector d are non zero vectors such that vector c =x1i + y1j + z1k and vector d =(y1z2y2z1)+(x1y2 x2y1)show that the two vectors are perpendicular. 
math
given that vectors(p+2q) and (5p4q) are orthogonal,if vectors p and q are the unit vectors,find the product of vectors p and q? 
math
given that vectors(p+2q) and (5p4q) are orthogonal,if vectors p and q are the unit vectors,find the dot product of vectors p and q? 
Math: Trig
Help with vectors, please. Thanks 1) Express point in rectangular form. Give EXACT answer, if possible? 
Please Help asap for math
Given the following: vector u= [2,1,2] and vector v=[1,1,4] and vector w= [4,3,2] find: a)theta, the angle between vectors, u and w. b)Are the vectors, u, v, and w coplanar?