Homework Answers
The given table, duly completed is as under:
|
U |
P5 |
P8 |
Pn |
|
Dim(U) |
6 |
9 |
n+1 |
|
Rank(T) |
0 |
4 |
n-6 |
|
Nullity (T) |
6 |
5 |
7 |
Note:
The rank plus nullity equals the dimension of the domain. Also, the set {1,x,x2,…,xn} is trhe standard basis of Pn so that dim(Pn) = n+1.
Add Answer to:
CHALLENGE ACTIVITY 5.5.1: Rank and nullity of a linear transformation. Jump to level 1 1 2...
Lienar CHALLENGE ACTIVITY 5.5.1: Rank and nullity of a linear transformation. Jump to level 1 1...
Lienar
CHALLENGE ACTIVITY 5.5.1: Rank and nullity of a linear transformation. Jump to level 1 1 2 Let T: U + V be a linear transformation. Use the rank-nullity theorem to complete the information in the table below. 3 R2x1 R2x2 4 R5x3 Ex: 5 2 Ex: 5 U dim(U) rank(T) nullity(T) 1 Ex: 5 Ex: 5 3 3 7 2. 3 Check Next Feedback?
Linear CHALLENGE ACTIVITY 5.7.1: Matrix representation with respect to nonstandard bases. Jump to level 1 1...
Linear
CHALLENGE ACTIVITY 5.7.1: Matrix representation with respect to nonstandard bases. Jump to level 1 1 2 Let T : R3 + R2 be defined by T (6)-1 = 2x1 - 22 3x3 3 6 0 3 4 Let B uj = 7 , U2 , U3 2 and C= {v} = [:'], x==(-2]} What augmented matrix should be used to find (T]%, the matrix representation of T with respect to the bases B and C. Ex: 5 2 3...
Hint: Apply the rank-nullity theorem to the linear map Pn → Rn+1 that sends p ?→...
Hint: Apply the rank-nullity theorem to the linear map Pn → Rn+1
that sends p ?→
(p(x0), . . . , p(xn)). Then use the fact that if polynomial of
degree ≤ n has n + 1 distinct roots, then it is the zero
polynomial.
(3 points) Application: polynomial interpolation. Let (20; yo), ..., (In; Yn) be n +1 points R2 with distinct x-coordinates. Show that there exists a unique polynomial p(t) of degree <n such that p(xi) = yi...
Problem 3. Let V and W be vector spaces, let T : V -> W be...
Problem 3. Let V and W be vector spaces, let T : V -> W be a linear transformation, and suppose U is a subspace of W (a) Recall that the inverse image of U under T is the set T-1 U] := {VE V : T(v) E U). Prove that T-[U] is a subspace of V (b) Show that U nim(T) is a subspace of W, and then without using the Rank-Nullity Theorem, prove that dim(T-1[U]) = dim(Unin (T))...
:| Let T : P → R , such that T (ao +ax+a2x2 +a3r)-4 +ai +a, +a3 . a) Prove that T is a linear transformation b) Find the rank and nullity of T. c) Find a basis for the kernel of T. :| Let T : P...
:| Let T : P → R , such that T (ao +ax+a2x2 +a3r)-4 +ai +a, +a3 . a) Prove that T is a linear transformation b) Find the rank and nullity of T. c) Find a basis for the kernel of T.
:| Let T : P → R , such that T (ao +ax+a2x2 +a3r)-4 +ai +a, +a3 . a) Prove that T is a linear transformation b) Find the rank and nullity of T. c) Find a...
CHALLENGE ACTIVITY 5.7.1: Hypothesis test for the difference between two population means. > Jump to level...
CHALLENGE ACTIVITY 5.7.1: Hypothesis test for the difference between two population means. > Jump to level 1 The mean voltage and standard deviation of 5 batteries from each manufacturer were measured. The results are summarized in the following table. Manufacturer Sample mean voltage (millivolts) Sample standard deviatio A 167 B 164 3 What type of hypothesis test should be performed? Select What is the test statistic? Ex: 0.123 What is the number of degrees of freedom? Ex 250 Does sufficient...
linear algebra Recall the Rank Theorem, which states that if A is an mxn matrix, then...
linear algebra
Recall the Rank Theorem, which states that if A is an mxn matrix, then rank(A) + nullity(A) = n. Recall the given matrix A. A = [ 3 -6 0 3 11 -1 2 1 3 6 [ 2 -4 1 6 7 This is a 3 x matrix, so n = . Furthermore, we previously determined that rank(A) - 2. Substitute these values into the formula from the Rank Theorem and solve for nullity(A). rank(A) + nullity(A)...
CHALLENGE ACTIVITY 5.7.1: Hypothesis test for the difference between two population means. Jump to level 1...
CHALLENGE ACTIVITY 5.7.1: Hypothesis test for the difference between two population means. Jump to level 1 An electrician wants to know whether batteries made by two manufacturers have significantly different voltages. The voltage of 130 batteries from each manufacturer were measured. The population standard deviations of the voltage for each manufacturer are known. The results are summarized in the following table. 3 Manufacturer Sample mean voltage (millivolts) Population standard deviati A 197 4 B 196 2 What type of hypothesis...
I know theorem states that rank T = Mdb(T). but what is next? Thank you very...
I know theorem states that rank T = Mdb(T). but what
is next?
Thank you very much
2. (8 marks) Let dim V = dim W = n. Let T:V → W be a linear transformation of rank k. Show that there are ordered bases B of V and D of W such that MdB(T) is a matrix that contains exactly k entries that are ls (with the rest being Os).
Request for the answers with proofs for the below questions? I know for Answer to Question 2 is 1<=nullity(A)<=n....
Request for the answers with proofs for the below questions?
I know for Answer to Question 2 is 1<=nullity(A)<=n. But
not confident on the answer.
Question2 If Aisamx n matrix, what are the possible values of nullity(A)? (m-1) nullity A) nullitylA)Sn nullitylA)-O nullityA)2 m 4 Previous Question 3 For what values of "a does matrix 0 1 have rank 2? O a-3/2 a-2/5 uestion 4 et A be k x k matrix with real entries and x # 0. Then...
Lienar
CHALLENGE ACTIVITY 5.5.1: Rank and nullity of a linear transformation. Jump to level 1 1 2 Let T: U + V be a linear transformation. Use the rank-nullity theorem to complete the information in the table below. 3 R2x1 R2x2 4 R5x3 Ex: 5 2 Ex: 5 U dim(U) rank(T) nullity(T) 1 Ex: 5 Ex: 5 3 3 7 2. 3 Check Next Feedback?
Linear
CHALLENGE ACTIVITY 5.7.1: Matrix representation with respect to nonstandard bases. Jump to level 1 1 2 Let T : R3 + R2 be defined by T (6)-1 = 2x1 - 22 3x3 3 6 0 3 4 Let B uj = 7 , U2 , U3 2 and C= {v} = [:'], x==(-2]} What augmented matrix should be used to find (T]%, the matrix representation of T with respect to the bases B and C. Ex: 5 2 3...
Hint: Apply the rank-nullity theorem to the linear map Pn → Rn+1
that sends p ?→
(p(x0), . . . , p(xn)). Then use the fact that if polynomial of
degree ≤ n has n + 1 distinct roots, then it is the zero
polynomial.
(3 points) Application: polynomial interpolation. Let (20; yo), ..., (In; Yn) be n +1 points R2 with distinct x-coordinates. Show that there exists a unique polynomial p(t) of degree <n such that p(xi) = yi...
Problem 3. Let V and W be vector spaces, let T : V -> W be a linear transformation, and suppose U is a subspace of W (a) Recall that the inverse image of U under T is the set T-1 U] := {VE V : T(v) E U). Prove that T-[U] is a subspace of V (b) Show that U nim(T) is a subspace of W, and then without using the Rank-Nullity Theorem, prove that dim(T-1[U]) = dim(Unin (T))...
:| Let T : P → R , such that T (ao +ax+a2x2 +a3r)-4 +ai +a, +a3 . a) Prove that T is a linear transformation b) Find the rank and nullity of T. c) Find a basis for the kernel of T.
:| Let T : P → R , such that T (ao +ax+a2x2 +a3r)-4 +ai +a, +a3 . a) Prove that T is a linear transformation b) Find the rank and nullity of T. c) Find a...
CHALLENGE ACTIVITY 5.7.1: Hypothesis test for the difference between two population means. > Jump to level 1 The mean voltage and standard deviation of 5 batteries from each manufacturer were measured. The results are summarized in the following table. Manufacturer Sample mean voltage (millivolts) Sample standard deviatio A 167 B 164 3 What type of hypothesis test should be performed? Select What is the test statistic? Ex: 0.123 What is the number of degrees of freedom? Ex 250 Does sufficient...
linear algebra
Recall the Rank Theorem, which states that if A is an mxn matrix, then rank(A) + nullity(A) = n. Recall the given matrix A. A = [ 3 -6 0 3 11 -1 2 1 3 6 [ 2 -4 1 6 7 This is a 3 x matrix, so n = . Furthermore, we previously determined that rank(A) - 2. Substitute these values into the formula from the Rank Theorem and solve for nullity(A). rank(A) + nullity(A)...
CHALLENGE ACTIVITY 5.7.1: Hypothesis test for the difference between two population means. Jump to level 1 An electrician wants to know whether batteries made by two manufacturers have significantly different voltages. The voltage of 130 batteries from each manufacturer were measured. The population standard deviations of the voltage for each manufacturer are known. The results are summarized in the following table. 3 Manufacturer Sample mean voltage (millivolts) Population standard deviati A 197 4 B 196 2 What type of hypothesis...
I know theorem states that rank T = Mdb(T). but what
is next?
Thank you very much
2. (8 marks) Let dim V = dim W = n. Let T:V → W be a linear transformation of rank k. Show that there are ordered bases B of V and D of W such that MdB(T) is a matrix that contains exactly k entries that are ls (with the rest being Os).
Request for the answers with proofs for the below questions?
I know for Answer to Question 2 is 1<=nullity(A)<=n. But
not confident on the answer.
Question2 If Aisamx n matrix, what are the possible values of nullity(A)? (m-1) nullity A) nullitylA)Sn nullitylA)-O nullityA)2 m 4 Previous Question 3 For what values of "a does matrix 0 1 have rank 2? O a-3/2 a-2/5 uestion 4 et A be k x k matrix with real entries and x # 0. Then...
Most questions answered within 3 hours.
-
This is C++ code for parking fee management program
#include <iostream>
#include <iomanip>
using namespace std;...
asked 4 minutes ago -
The free energy change for the following reaction at 25 °C, when
[Sn2+] = 1.17 M...
asked 1 hour ago -
An MNE is this kind of industry when competition in one country
is essentially independent of...
asked 3 hours ago -
. For this set of questions, determine what
proportion of a normal distribution is located betweeneach...
asked 3 hours ago -
A college student is employed as a door-to-door newspaper
salesman. Historical data suggests that the student...
asked 4 hours ago -
MATLAB HW 11 problem using Switch Case and Input commands
Write a script file that calculates...
asked 4 hours ago -
Considering gravitational time dilation, calculate the time that
passes in Earth’s surface while 1 hour passes...
asked 5 hours ago -
Minitab Problem: Take the Lake Hume June rainfall data and find
use the processes outlined in...
asked 6 hours ago -
X Company is trying to decide whether to continue using old
equipment to make Product A...
asked 6 hours ago -
IN PYTHON ONLY !! Program 2: Re-work
program #5 (WeeklyHours) from the previous assignment such that...
asked 6 hours ago -
The average length of time between arrivals at a turnpike
toll-booth is 26 seconds. What is...
asked 8 hours ago -
(a) A piston at 6.1 atm contains a gas that occupies a volume of
3.5 L....
asked 9 hours ago