Determine which of these sets spans R^3
q) (1,0,1) , (3,1,0), (-1,0,0),(2,1,5)
x) (2,1,2) , (1,1,1), (-3,0,-3)
y) (-1,2,1),(4,1,-3),(-6,3,5)
z) (1,0,0),(0,2,0),(1,2,0),(0,-1,1)
a) only q
b)q and x
c) q and z
d) only z
Apply the KKT conditions to determine whether or not the
solution XT = (1,1,1) is optimal for the following problem:
minimize 2X1 + X2^3 + X3^2
subject to
2X1^2 + 2X2^2 + X3^2 >=4
X1, X2, X3 >=0
Determine whether S is a basis for
R3.
S = {(4, 2, 5), (0, 2, 5), (0, 0, 5)}
S is a basis for R3.S is
not a basis for R3.
If S is a basis for R3, then write
u = (8, 2, 15) as a linear combination of the
vectors in S. (Use s1,
s2, and s3, respectively,
as the vectors in S. If not possible, enter
IMPOSSIBLE.)
u =
In the real vector space R 3, the vectors u1
=(1,0,0) and u2=(1,2,0) are known to lie in the span W of the
vectors w1 =(3,4,2), w2=(0,1,1), w3=(2,1,1) and w4=(1,0,2). Find
wi, wj ?{w1,w2,w3,w4} such that W = span({u1,u2,wk,wl}) where
{1,2,3,4}= {i,j,k,l}.
Use a scatterplot and the linear correlation coefficient r r to
determine whether there is a correlation between the two variables.
(Note: Use software, and don't forget to look at the scatterplot!)
x 0.6 1.1 2.3 3.1 4.7 5.9 6.5 7.3 8.9 9.2 10.9 11.9 12.8 13.6 14.6
y 15.5 13.9 10.9 13.4 10.8 11.1 10.4 5.7 4.3 3.8 6 4.5 4.2 -0.4 0.1
(a) r= r= equation editor Equation Editor (b) There is A. a
positive correlation between x...
Please answer in C++
Given 3 numbers T, r and s, where r != s and r > 1 & s
> 1. Print a list of numbers from 1 to T where numbers divisible
by r whose decimal representation does not contain the digit r
should be replaced by the number 555 and any number (int) divisible
by s whose decimal representation does not contain the number s
should be replaced by the number 333. Numbers for which both...
For each of the following determine whether ∗ is a binary
operation on R. If so, determine whether or not ∗ is associative,
commutative, has an identity element, and has inverse elements.
(a) a ∗ b = (ab) / (a+b+1)
(b) a ∗ b = a + b + k where k ∈ Z
(c) a ln(b) on {x ∈ R | x > 0}