Linear algebra Definition and 999 Threads

Homework Statement The matrix given is row 1: [0,1] row 2: [1,0] The matrix above if you switch row 1 with row 2 is just the identity matrix. So wouldn't that matrix already be the inverse of the identity matrix? Homework Equations The Attempt at a Solution

Author: Jim Hefferon Title: Linear Algebra Download Link: http://joshua.smcvt.edu/linalg.html Prerequisities: Table Of Contents: Linear Systems Solving Linear Systems Gauss’s Method Describing the Solution Set General=Particular+Homogeneous Linear Geometry Vectors in Space...

Homework Statement Explain why each of the following algebraic rules will not work in general when the real numbers a and b are placed by nxn matrix A and B (a+b)2=a2+2ab+b2 This question is a bit confusing to me and I have no idea how to even start this problem Homework Equations...

Author: Stephen Friedberg, Arnold Insel, Lawrence Spence Title: Linear Algebra Amazon link https://www.amazon.com/dp/0130084514/?tag=pfamazon01-20 Prerequisities: Being acquainted with proofs and rigorous mathematics. Knowing what matrices and determinants are, is also helpful. Level...

Author: G.E. Shilov Title: Linear Algebra Amazon link https://www.amazon.com/dp/048663518X/?tag=pfamazon01-20 Prerequisities: Being acquainted with proofs and rigorous mathematics. Knowing what matrices and determinants are, is also helpful. Level: Undergrad Table of Contents...

Author: David Poole Title: Linear Algebra: A Modern Introduction Amazon Link: https://www.amazon.com/dp/0538735457/?tag=pfamazon01-20 Prerequisities: Table of Contents: Vectors Introduction: The Racetrack Game The Geometry and Algebra of Vectors Length and Angle: The Dot Product...

Well, I am a second year astrophysics student in the UK. However, I want to go for a PHD in theoretical physics after my graduation. So I believe I have to take more maths modules as much as possible. I have taken mathematical techniques 1 and 2 which cover up to vector calculus, differential...

Homework Statement Let A be a 5x3 matrix. If b=a1+a2=a2+a3 then what can you conclude about the number of solutions of the linear system Ax=b? Explain I don't have the solution for this problem, and my first thinking was the system would be overdertermined, and be most likely...

Author: Steven Roman Title: Advanced Linear Algebra Amazon link https://www.amazon.com/dp/0387728287/?tag=pfamazon01-20 Prerequisities: Having completed at least one year of proof based linear algebra. Basic abstract algebra, in particular group and ring theory, is also assumed. Level...

Homework Statement Find all polynomials of the form a + bx + cx^2 that: Goes through the points (1,1) and (3,3) and such that f'(2) = 1Homework Equations a + bx + cx^2 f'(x) = x+2cx f'(2) = 2 + 4c polynomial through (1,1) = a + b1 + c1 = 1 polynomial through (3,3) = a + b3+ c3^2 = 3 The...

Hey guys, lurked here a bit, but now I'm in this new math course right. So anyway it seems like a completely new language to me. There's some discussions about reduced row echelon form in the textbook I'm using. I was taught (before going into the course) that the object was to get leading 1s in...

Homework Statement I have attached the relevant question as an image (for sake of ease) Homework Equations The Attempt at a Solution Also attached, in blue. Thanks a lot for any help at all!

Homework Statement Let E1 = (1, 0, ... ,0), E2 = (0, 1, 0, ... ,0), ... , En = (0, ... ,0, 1) be the standard unit vectors of Rn. Let x1 ... ,xn be numbers. Show that if x1E1+...+xnEn=0 then xi=0 for all i. Homework Equations The Attempt at a Solution Proof By contradiction...

Hi, Homework Statement I wish to pose a few questions I have concerning transformations: (1) I am trying to disprove the following statement: Let T: V->U be a linear transformation between vector spaces V and U, and let {v1,...,vn} be a set of vectors in V. If {Tv1,...,Tvn} spans U, then...

I had a linear algebra course for my 1st year civil engineering curriculum, and I passed with a 3.2 GPA but I only conceptually understood about 10% of what was taught to me. I don't know what an eigenvalue/eigenvector is, what the hell is a subspace, nullspace, imagespace. What the hell is...

Hi everyone, I'm a grade 11 student in HS and am currently studying MV Calculus and Linear Algebra from distance learning through Stanford. Due to some problems, I'm going pretty slowly but I expect things to pick up soon. Anyway, I have an agreement with my school that if I complete a...

My school does not require physics majors to take linear algebra. I've noticed that some schools have a course called "differential equations and linear algebra" that is taken after the calc sequence but we only have to take ODE. There is a matrix theory class that math majors take that I've...

Hello, I just completed a math course that had a mixture of differential equations and linear algebra. The book used was Elementary Differential Equations with Linear Algebra by Rabenstein. Since the class covered both topics, of course we couldn't go into a lot of detail for either type of...

When did you guys really start to understand linear algebra? Like you understood why it worked and how it works instead of just "how." What did you read or do to get to that point. Reason why I'm asking is I got 4 weeks off and I'd really want to get better with linear algebra. I took one...

Can anyone recommend a good differential equations and linear algebra book? The books that I've read so far are Linear algebra: https://www.amazon.com/dp/0030103479/?tag=pfamazon01-20 Differential Equations: https://www.amazon.com/dp/0534373887/?tag=pfamazon01-20 I was able to get an...

A 3x3 symmetric matrix has a null space of dimension one containing the vector (1,1,1). Find the bases and dimensions of the column space, row space, and left null space. I understand how to get the Dim of Col(A), Row(A), and Nul(A^T) but how do i get the bases with just knowing the dimension...

I think I know the answer to these questions, but I just want to make sure. 1) If A is invertible then A+A is invertible. True/False True. Because det(A)≠0, det(A+A)=det(2A)=2^n * det(A)≠0 Is this correct. 2) A 3x3 matrix can have 2 distinct eigenvalues. True/False True, although...

hi all, i was given a take home exam for my linear algebra course and i can't seem to find the answer to this problem. Homework Statement if A^T\vec{b} = \vec{0} what can you say about ##\hat{b}## the vector in Col A which is the best approximation of ##\vec{b}##. Homework Equations ##A^T A...

Homework Statement Does the equation \text{rank}(A^T A = \text{rank}(A A^T) hold for all nxm matrices A? Hint: the previous exercise is useful.Homework Equations \text{ker}(A) = \text{ker}(A^T A) \text{dim}(\text{ker}(A) + \text{rank}(A) = m The Attempt at a Solution The previous exercise...

I just was wondering what would be the best way to begin preparing for a course in linear algebra. It is a upper division applied course. Also, how does linear algebra compare in, conceptual thinking compared to say Calculus 3? The course description is as follows: Solving linear systems...

I am currently a first year graduate student in math, and I am trying to pick a linear algebra book to work through during the winter break. I have already gone through the computational style linear algebra, and I have also gone through Axler's Linear Algebra Done Right. I would like to go...

Homework Statement I'm reading from the first edition of Axler's Linear algebra done right. In the section on sums of vector subspaces, he states: U = {(x,0,0) ∈ F3 | x ∈ F} W = {(y,y,0) ∈ F3 | y ∈ F} and 1.7 U + W = {(x,y,0) ∈ F3 | x,y ∈ F} However, shouldn't the answer be U...

Forgive me ahead of time, I don't really know how to use LaTeX, (it's on my to do list). Homework Statement Given the vector space C([0,pi]) of continuous, real valued functions on the given interval, as well as the inner product <f,g>=integral(f(t)*g(t))dt from 0 to pi: a) Prove the set...

Classify the abelian groups of order 32. a) In each case give the annihilator of the group along with dim_{Z_2} \frac{ker \mu_{2^s}}{ker \mu_{2^{s-1}}} for s=1,...,5. Where \mu_k(x) = kx for all k. b) If you know the annihilator of each of these groups, how many values of s (beginning...

| x 1 0 | | 0 x 1 | | 0 0 x | I need to raise this matrix to the 50th power. Of course I can not solve this the extremely long way. Here is my attempt at this: Let A represent the matrix above, and let N represent the following matrix: | 0 1 0 | | 0 0 1 | | 0 0 0 | Then A = XI +...

I'm a bit confused on how to do this problem, here is what I have. Part a) I must set up the set of linear differential equations with the initial values. Using the balance law gives y0'=0.2+0.1-0.2-0.1=0 The other 2 net rate of change would be equal to 0 as well. But...I don't think I did...

Matrix Alalysis, Matrix Algebra, Linear Algebra, they seem to cover many similar topics. Would someone explain about what are the differences between them? Thanks in advance.

Determinant -- best way of introducing determinants on a linear algebra course What is the best way of introducing determinants on a linear algebra course? I want to give real life examples of where the determinant is applied.

Hello, Is it true that the following system of linear equations would always have a single solution (i.e. would never have an infinite number of solutions nor none) for any value of λ? λx + 3y -z = 1 x + 2y -z = 2 -λx + y + 2z = -1 May someone kindly confirm?

There is a theorem in our textbook that says: Every abelian group G is a Z-module. Moreover, the Z-module structure on G is unique: for n ∈ Z and g ∈ G, ng is the n-th power of g in the group structure of G. (Thus, if n > 0, ng = g + · · · + g, the sum of n copies of g.) Finally, every group...

I want to beginning learning linear algebra. I will be studying it on my own, so I was wondering what the best book would be.

Homework Statement Hi there! First time user, so I hope I do this right. The question is: Let A be an 8x5 matrix of rank 3, and let b be a nonzero vector in N(AT). First, prove that the system Ax=b must be inconsistent. Then, how many least squares solutions will the system have...

Hi all, I was wondering which of these two courses is more difficult? I understand the standard caveat that it depends on the institution and the professor but I'm just wondering, in terms of sheer difficulty of the concepts taught in these two courses, is there a general consensus?

Homework Statement I am given the following vectors : p = 3 q = 2 r = 5 2 4 3 -4 -3 -1 They ask to find these: 1. a normal to the plane containing p, q and r. 2. the distance from the origin to the plane...

Suppose T belongs to L(V,V) where L(A,W) denotes the set of linear mappings from Vector spaces A to W, is such that every subspace of V with dimension dim V - 1 is invariant under T. Prove that T is a scalar multiple of the identity operator. My attempt : Let U be one of the sub spaces of V...

Hey guys, I'm studying these concepts in linear algebra right now and I was wanting to confirm that my interpretation of it was correct. One to one in algebra means that for every y value, there is only 1 x value for that y value- as in- a function must pass the horizontal line test (Even...

Homework Statement For a nonhomogeneous system of 2012 equations in 1999 unknowns, answer the following three questions: Can the system be inconsistent? Can the system have infinitely many solutions Can the system have a unique solutions? Homework Equations The Attempt at a...

Hello, I have been reading Linear Algebra mostly from the web. But still can anybody suggest me any free resource for a e-book or a hard copy book on Linear Algebra. On the web, amazon.com, there are so many books available, but I am looking for something which is a step by step guide...

1(a) Construct a 4*4 matrix whose determinant is easy to compute using cofactor expansion but hard to evaluate using elementary row operations. (b) Construct a 4*4 matrix whose determinant is easy to compute using elementary row operations but hard to evaluate using cofactor expansion

*new question, playing with projection matrix. Well I have a new question about the A(ATA)-1AT matrix. http://puu.sh/1jXT6 I was able to show that BT was idempotent, but my manipulation was a bit different from the teacher for B2 Let B2 = (A(ATA)-1AT)(A(ATA)-1AT) I did...

Homework Statement The problem is : Let S = [ (1,-1,3) , (-1,3, -7) , (2,1,0) ]. Do the vectors u = (5,1,3) and v = (2,3,6) belong to span(S) Homework Equations The Attempt at a Solution So span means that I could take linear combinations of u and v and they should end up...

Hello guys I'm despesrately looking for a link to download a book named as Linear Algebra Problem solvers REA, whatever edition it is. Thank you in advance

which books do you advise with to study linear algebra ? for beginners

Homework Statement Hi, I am really having trouble with questions regarding proving whether a given set is a vector space or not. So one of the questions is [ x ε R2|x12=x23 ] So I have to prove whether the following set is a vector space Homework Equations The Attempt at a...

Homework Statement Let E be the solid enclosed by the paraboloid z = x2 + y2 and the plane z = 9. Suppose the density of this solid at any point (x,y,z) is given by f(x,y,z) = x2. Homework Equations x2 + y2 = r2 = 9; r = 3 ∫∫∫E x2 The Attempt at a Solution The limit of z is...