Linear Algebra vector problems?
Given the vectors u =(1,2,3) and v = (2,3,1) in R3:
a. Find k so that w = (1,k,4) is a linear combination of u and v. [5]
b. Discuss the span of u, v, and w. [5]
Given the vectors u =(1,2,3) and v = (2,3,1) in R3:
a. Find k so that w = (1,k,4) is a linear combination of u and v. [5]
b. Discuss the span of u, v, and w. [5]
Comments
au = (a, 2a, 3a)
bv = (2b 3b, b)
a+2b = 1
2a + 3b = k
3a +b = 4
b = 4-3a
a + 2(4-3a) = 1
a+ 8 -6a = 1
-5a = -7
a = 7/5
b = 4 - 3(7/5) = 4-21/5 = -1/5
k = 2a + 3b = 14/5 -3/5 = -11/5