Answered: find the range, rank, ker and nullity…

find the range, rank, ker and nullity of the following linear transformation T:R^4 -> R^3 such that T(x1,x2,x3,x4) = (x1,-x4,x2+x3,x3-x4)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 5CM: Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).

See similar textbooks

Related questions

Q: Use the method of cylindrical shells (for all parts) to set up an integral (without the absolute val...

Q: Fourteen members of the executive committee of the Student Senate must vote for a student representa...

A: Given: The preference table is given below: To determine: The winner using Borda count method.

Q: [4 The (1,2) – entry of -1 07 3 0 is 1 3. 1 2 A) 14 B -1 4 D 1

Q: Q) Let Tright on R ? {(a, o0) : a € R}U {¢, R} . Prove that Tright is toplogy

Q: If A and B are nXn matrices, then (AB)²=A²B? A True

Q: [1 0 Which of the following values of a will make |2 2 ... non-invertible? lo 2 -a. A) 5 B) 0 c) 4 D...

A: correct option is C.4

Q: Let T : R3 - R be a linear transformation. If Т3, 2, — 1) 3D (3, 5) and T(1, –2, 3) = (3, –2) what i...

Q: Use the definition of the Laplace transform to find L{cos(at)} where a is a constant. You must use t...

Q: Number of votes 13 12 11 se that the Borda count method is used on the following preference table. I...

A: We can give 3 points to the first choice, two points to the second choice, and 1 point to the third ...

Q: A teacher wants to assign 4 different tasks to her 4 students. In how many possible ways can she do ...

Q: Which of the following matrices corresponds to the elementary row operation 3R1 + R2 → R2 on-a 3x3 ш...

A: We want to find matrix with given operation

Q: 2 Which of the following values of a will make |2 0 a non-invertible? -al

Q: Find the third term of: (z+3)2n Σ-0(-1)"+1 (2n)! O [(z-3)^8]/40320 O [(z-3)^2]/2 O [(z-3)^4]/24 O [(...

Q: Find the curvature and the radius of curvature of the curve r(t) = 3 cos ti +4 sin tj + tk at t = T/...

A: The general form of the equation of a curve in three-dimensional space is given by r(t)=f(t)i+g(t)j+...

Q: Pls help ASAP.

Q: Let A and B be 3 × 3 matrices such that A 3 = B 6|. The matrix C = A – 2B is invertibl A) True False

Q: Let f_n(x)= nx / 1+nx^2. Find the pointwise limit of (f_n) for all x in (0,infinity). Is the conv...

A: Given : fn(x)=nx1+nx2 .

Q: calculate inverse Laplace transform ln(1+w2/s2) answer image

Q: Solve xy (1 + xy) = dy = 1. dx dy dx +x sin 2y =x° cos2 y. %3D · Solve

Q: 3 6. Show that [[[ y sinzdxdydz = (1– cos1). 2 COS %3D 00

A: We have to prove given integral

Q: Proe the tollowing Statement . Fa dyer n22, n'3 is. never dinsible by 4. any thint. comosder h as od...

Q: Consider the graph of f(x) = 6x-. y + 3 2-

Q: Problem 1: Prove that any (simple) graph with |E| < |V| –- 1 is disconnected.

A: We know that the minimally connected graph of n vertices is a tree. A tree with n vertices has (n-1...

Q: For the function h (x) = (2x + 1)° find two functions, f and g, such that h (x) = f (g (x)). O a) f ...

Q: A small country with a population of 8,000,000 consists of four states, A, B, C, and D. There are 16...

A: (a) Given standard divisor is 50,700, using this we need to find the modified quota.

Q: Find the mass and center of mass of the lamina that occupies the region D and has the given density ...

A: Here given D is the triangle having vertices 0, 0, 2, 1 and 0, 3 And density function is ρx, y=5x+y...

Q: Let G = A4 and H = (1 2 3)). a) Find the left cosets of H in G. b) Find the right cosets of H in G. ...

Q: O Let A be an m x n matrix, and let B be the result of performing a single elementary row operation ...

Q: Is there a one-to-one correspondence between the points on a 2-inch line segment and the points on a...

Q: A boat manufacturer has 152 new boats of a new model to be apportioned to four dealerships. The manu...

A: (a) To find the standard divisor divide the total number of annual sales by the number of new boats....

Q: Find the standard form of the equation of the hyperbola shown below. The standard form of the equati...

Q: Determine the solutions of the equation valid near the origin for x>0? 2xy''+6y'+y=0

A: Given differential equation is 2xy''+6y'+y=0 (1) Comparing with y''+Py'+Qy=0 Here P=3x...

Q: Find the moments of inertia, I, ly, and I, for the rectangular region D: {(x, y)| 1<x< 3,1 < y < 4}x...

Q: The preference table for an election is given. Suppose that the Borda count method is used on the ta...

Q: 3. Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. (a) How many pairs (f, g) E ...

Q: Using Upper and Lower Sums In Exercises 37 and 38, bound the area of the shaded region by approxinma...

A: Lower and upper sum of the function

Q: x +3, (x + 3)2 + 22 1+- 32

Q: Theorem 3.2.10. Let ICR be an open interval, let e E1, let f, g:1-{c}-R be functions and let keR. Su...

Q: 83 voters are asked to rank four brands of cereal: A, B, C, and D. The votes are summarized in the p...

A: If there is no majority then we eliminate the choices with fewer first-choice votes and then we redi...

Q: determine the inverse laplace transform of the function 1. 3/s+2 2. s+4/s^2+4

A: 1. Given, 3s+2

Q: Decide whether the following statement makes sense (or is clearly true) or does not make sense (o...

Q: The hypotenuse of a right triangle is 34 cm. find the length of the shortest leg if it is 14 cm shor...

Q: c) Convert the following expression to operator prefix notation, and draw the derivation tree. 7*3-3...

Q: Let o be a fixed odd permutation in Sn. Show that every odd permutation in Sn can be written as a pr...

Q: (-글 +V) Evaluate the given equation z (bar) where z = Answer: a. - b.-- V 1 C. d. 을 +

Q: The auxiliary equation for the given differential equation has complex roots. Find a general solutio...

A: Given : y"-4y'+20y = 0 To find : To find general solution

Q: Use Truth Tables to determine if the following statements are logically equivalent to each other. p ...

Q: If f(z) = ev8=rl then the simplify form of f(z) is: A) f(z) = ie-2vz B) f(z) = -i e?v2 C) f(z) = e?v...

A: Given function is fz=e8−πi. We have to find the simplify form of fz. We know that eix=cosx+isinx Now...

Q: (a) How many pairs (f, g) E F x F are there so that go f(1) = 1? Explain.

A: The main objective is to give explanation for part (a) why possible g functions are 4^3.

Q: There are 4 different Mathematics books and 5 different Science books. In how many ways can the book...

A: Total number of ways that the books can be arranged is 5760

Question

find the range, rank, ker and nullity of the following linear transformation T:R^4 -> R^3 such that T(x1,x2,x3,x4) = (x1,-x4,x2+x3,x3-x4)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find T(7,2).
Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.
Let T be a linear transformation from R3 into R such that T(1,1,1)=1, T(1,1,0)=2 and T(1,0,0)=3. Find T(0,1,1)
A translation in R2 is a function of the form T(x,y)=(xh,yk), where at least one of the constants h and k is nonzero. (a) Show that a translation in R2 is not a linear transformation. (b) For the translation T(x,y)=(x2,y+1), determine the images of (0,0,),(2,1), and (5,4). (c) Show that a translation in R2 has no fixed points.
Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a the kernel of T and b the range of T. c Determine the rank and nullity of T.
Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
For the linear transformation from Exercise 38, find a T(0,1,0,1,0), and b the preimage of (0,0,0), c the preimage of (1,1,2). Linear Transformation Given by a Matrix In Exercises 33-38, define the linear transformation T:RnRmby T(v)=Av. Find the dimensions of Rnand Rm. A=[020201010112221]
For the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the preimage of (0,0). Linear Transformation Given by a Matrix In Exercises 33-38, define the linear transformations T:RnRm by T(v)=Av. Find the dimensions of Rn andRm. A=[0110]
Let T:P2P3 be the linear transformation T(p)=xp. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3}.
Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and nullity of T. (b) Find a basis for the kernel of T.
Let T:P2P4 be the linear transformation T(p)=x2p. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3,x4}.