1) A) Write v as a linear combination of u1, u2, and u3, if possible. (Enter...

1)

A) Write v as a linear combination of u₁, u₂, and u₃, if possible. (Enter your answer in terms of u₁, u₂, and u₃. If not possible, enter IMPOSSIBLE.)

v = (−1, 7, 2), u₁ = (2, 1, 5), u₂ = (2, −3, 1), u₃ = (−2, 3, −1)

B) Write v as a linear combination of u and w, if possible, where u = (1, 3) and w = (2, −1). (Enter your answer in terms of u and w. If not possible, enter IMPOSSIBLE.)

v = (−3, −9)

C) Find w such that 2u + v − 3w = 0.

u = (0, 0, −6, 2),

v = (0, −3, 5, 1)

Expert Solution

Colby Messinger answered 1 year ago

#1 (a) Express, if possible,b= (7,8,9) as a linear combination of u1= (2,1,4),u2= (1,−1,3),u3= (3,2,5) (b)...

#1 (a) Express, if possible,b= (7,8,9) as a linear combination of u1= (2,1,4),u2= (1,−1,3),u3= (3,2,5) (b) What is Span{u1,u2,u3}? (c) Is the set{u1,u2,u3}linearly independent? #2 Considerv1= (1,2,1,1),v2= (1,1,3,1) and v3= (3,5,5,3). Find a homogeneoussystem the solution of which is Span{v1,v2,v3}. (Hint: Consider x= (x1, x2, x3, x4) where x=sv1+tv2+rv3 and look for conditions on x1, . . . , x4 where this system is consistent)

Consider a systematic (7,4) code whose parity-check equations are: v0=u0+u1+u2 v1=u1+u2+u3 v2=u0+u2+u3 where u0 u1 u2...

Consider a systematic (7,4) code whose parity-check equations are: v0=u0+u1+u2 v1=u1+u2+u3 v2=u0+u2+u3 where u0 u1 u2 and u3 are message digits and v0 v1 and v2 are parity-check digits. a) Find the generator and parity-check matrices for this code. b) Construct an encoder circuit for the code. c) Find the codewords corresponding to the binary messages (1001), (1011), and (1110).

Let B = {u1,u2} where u1 = 1 and u2 = 0 0 1 and...

Let B = {u1,u2} where u1 = 1 and u2 = 0 0 1 and B' ={ v1 v2] where v1= 2 v2= -3 1 4 be bases for R2 find 1.the transition matrix from B′ to B 2. the transition matrix from B to B′ 3.[z]B if z = (3, −5) 4.[z]B′ by using a transition matrix 5. [z]B′ directly, that is, do not use a transition matrix

(d) Given a condition with three different wind velocities, u1, u2 and u3 fluctuating towards a...

(d) Given a condition with three different wind velocities, u1, u2 and u3 fluctuating towards a base station, which have different heights, let say z1 , z2 and z3. Apply the correlation function between of the condition of the velocities and wind loads at the various heights.

I have three urns, U1, U2 and U3, such the first urn contains w1 identical white...

I have three urns, U1, U2 and U3, such the first urn contains w1 identical white balls and b1 identical black balls, the second urn contains w2 identical white balls and b2 identical black balls, and the third urn contains w3 identical white balls and b3 identical black balls. I first choose a ball uniformly at random from U1 (i.e., every ball is equally likely to be picked) and drop it into U2. Next, I pick a ball uniformly at...

1. Show that if λ1 and λ2 are different eigenvalues of A and u1 and u2...

1. Show that if λ1 and λ2 are different eigenvalues of A and u1 and u2 are associated eigenvectors, then u1 and u2 are independent. More generally, show that if λ1, ..., λk are distinct eigenvalues of A and ui is an eigenvector associated to λi for i=1, ..., k, then u1, ..., uk are independent. 2. Show that for each eigenvalue λ, the set E(λ) = {u LaTeX: \in∈Rn: u is an eigenvector associated to λ} is a subspace...

1)Test hypothesis? 2)Do we accept or Reject? H0: U1-U2=0 H1: U1-U2>0 X1: 501051 S1: 4000.64 X2:...

1)Test hypothesis? 2)Do we accept or Reject? H0: U1-U2=0 H1: U1-U2>0 X1: 501051 S1: 4000.64 X2: 52299.17 S2: 4000.01 N1: 2495 N2:2498

Given the vectors u1 = (2, −1, 3) and u2 = (1, 2, 2) find a...

Given the vectors u1 = (2, −1, 3) and u2 = (1, 2, 2) find a third vector u3 in R3 such that (a) {u1, u2, u3} spans R3 (b) {u1, u2, u3} does not span R3

Person A, B, and C have utility functions of U1=(R+6)c1, U2=(R+4)c2, and U3=(R+2)c3, budgets are I1,...

Person A, B, and C have utility functions of U1=(R+6)c1, U2=(R+4)c2, and U3=(R+2)c3, budgets are I1, I2, I3, c=expenditures on everything else R=1 is the house is purchased, 0 otherwise. What is the most each of the is willing to contribute to the house? If I1=5,800 I2=3,500 and I3= 2,100 would they buy the house at $4000 explain

1.let {v=(1,2,3,5,9),v2=(3,1,2,8,9),v3=(2,-5,5,9,4)} and {u1=(0,1,1,1,2),u2=(0,2,-2,-2,0)} be basis of subspaces V and U of R5 respectively.find a basis...

1.let {v=(1,2,3,5,9),v2=(3,1,2,8,9),v3=(2,-5,5,9,4)} and {u1=(0,1,1,1,2),u2=(0,2,-2,-2,0)} be basis of subspaces V and U of R5 respectively.find a basis and the dimension of V+U and V intersection U. 2.does a matrix have a right inverse ?if so find one A=[2,-3,-7,11;3,-1,-7,13;1,2,0,2] 3.find the interpolating polynomial that passes through the point (1,2),)(-1,-8) and (2,1)

Question