Suppose x1, x2, x3, x4 is linearly independent in V . Prove that
x1 − x2,...
Suppose x1, x2, x3, x4 is linearly independent in V . Prove that
x1 − x2, x2 − x3, x3 − x4, x4 is also linearly independent in V
For the linearly independent vectors
w1 =[ 0, 1, 0, 1 ] w2 =[1, 2, 0 ,0...
For the linearly independent vectors
w1 =[ 0, 1, 0, 1 ] w2 =[1, 2, 0 ,0 0] w3 = [0 , 2
, 1, 0]
(a) Use the Gram-Schmidt procedure to generate an orthonormal
basis.
Apply Gram-Schmidt in L2[−1,1] to the list of functions
1,x,x2,x3. (You do not have to normalize.)
Apply Gram-Schmidt in L2[−1,1] to the list of functions
1,x,x2,x3. (You do not have to normalize.)
Are the following functions linearly independent or dependent on
the interval (-∞, ∞)?
(a) cosh x,...
Are the following functions linearly independent or dependent on
the interval (-∞, ∞)?
(a) cosh x, sinh x, cosh2x
(b) (x-1)2 , (x+1)2 , x
Using wrongskian method
Determine if vectors are linearly dependent or
independent:
1. (1,2), (-1,-3)
2. (2,-1,4),(4,-2,7),(1,5,8)
3. (-3,4,2),(7,-1,3),(1.1.8)
Determine if vectors are linearly dependent or
independent:
1. (1,2), (-1,-3)
2. (2,-1,4),(4,-2,7),(1,5,8)
3. (-3,4,2),(7,-1,3),(1.1.8)
1. (a) Construct a Pearson’s χ 2 test for H0 : (X1, X2, X3, X4)
has...
1. (a) Construct a Pearson’s χ 2 test for H0 : (X1, X2, X3, X4)
has multinomial distribution with parameters (θ1, 3θ1, θ2, 1 − 4θ1
− θ2) against HA : (X1, X2, X3, X4) has some other multinomial
distribution, at the significance level α = 0.05. (b) Apply the
test in (a) to the data X = (26, 52, 34, 18
Determine if the set of functions is linearly independent:
1. f1(x)=cos2x, f2(x)=1, f3(x)=cos^2 x
2. f1(x)=e^...
Determine if the set of functions is linearly independent:
1. f1(x)=cos2x, f2(x)=1, f3(x)=cos^2 x
2. f1(x)=e^ x, f2(x)=e^-x, f3(x)=senhx
x1-5x2+x3+3x4=1
2x1-x2-3x3-x4=3
-3x1-3x3+7x3+5x4=k
1 ) There is exactly one real number k for which the system...
x1-5x2+x3+3x4=1
2x1-x2-3x3-x4=3
-3x1-3x3+7x3+5x4=k
1 ) There is exactly one real number k for which the system has
at least one solution; determine this k and describe all solutions
to the resulting system.
2 ) Do the solutions you found in the previous part form a
linear subspace of R4?
3 ) Recall that a least squares solution to the system of equations
Ax = b is a vector x minimizing the length |Ax=b| suppose that
{x1,x2,x3,x4} = {2,1,1,1}
is a...