Linear algebra Definition and 999 Threads

Please help me to understand the solution :( (I have made the sketch, is it correct?, where has the 1/4 comes from? is it like 1:3 (1 ratio 3) => numerator divided by numerator + denominator = 1/1+3 =1/4 (as given on page 6 at http://www.lowndes.k12.ga.us/view/14167.pdf )? or am I wrong? For...

I'm interested in learning how to solve a relatively general sort of problem that comes up a lot in my problem sets and will presumably come up in future exams. I'm asked to give an example of a matrix or linear transformation that has a given image or kernel. Here are some examples...

After having covered single variable calculus to a rather thorough degree, I would now like to move forward to linear algebra. As such I would like to enquire as to any recommendations for a text appropriate for what is essentially a beginner to the subject (I have received very basic...

Homework Statement I = Identity matrix Suppose that A^2 = A. Prove that I - 2A = (I - 2A)^-1 Homework Equations ahh don't know what to put here The Attempt at a Solution So I have to prove this thing is it's own identity... interesting.. I - 2A = I - 2A^2 (I - 2A^2)*(I - 2A)^-1...

Thanks.

I am a math major currently in a community college reputed for having an outstanding math department, lucky me :D. I am taking Calculus 2 this semester. Next semester I'll be taking Calculus 3 with linear algebra or discrete math. Can I take all three at the same time or would it be an overkill...

Let $$A(2,-1,1)$$, $$B$$ and $$C$$ be the vertices of a triangle where $$\overrightarrow{AB}$$ is parallel to $$\vec{v}=(2,0,-1), $$$$\overrightarrow{BC}$$ is parallel to $$\vec{w}=(1,-1,1)$$ and $$\angle(BAC)=90°$$. Find the equation of the line through $$\(A\)$$ and $$\(C\)$$ in vector and...

So, I'm interested in using my knowledge of elementary linear algebra (I can do projections, rotations, diagonalization, find eigenvalues/states/vectors, and a couple of other things) to learn other things based off of it. Is there an 'advanced linear algebra' sort of class? My institution...

So I had a quiz on Wednesday and got the problem wrong but don't know why. The question is: Use elementary row operations to reduce the matrix A= 3 1 -1 2 3 1 -4 0 2 to upper-triangular form. Each of these elementary row operations should have the form...

I was placed into honors calculus III for school. I was happy about this and I consider myself to be a pretty quick learner in math. However, my teacher is using many notations and terms that I am completely unfamiliar with. Mostly, I believe, because I've never taken linear algebra. I am...

Homework Statement Homework Equations A = SDS-1 Under some specific conditions, An=SDnS-1 The Attempt at a Solution det(A-λI) = 0 (16-λ)(-λ) - (-64)(1) = 0 λ2 - 16λ + 64 = 0 λ = 8 Multiplicity 2. This is as far as I got because you need 2 eigenvalues to get 2...

I am trying to self study linear algebra. This might seem like a very silly question but what does R subscript 3 mean in the context of linear algebra. I am NOT talking about R ^ 3 which is 3 dimensional vector space

Why do we need fields (Why do we define fields?)for linear algebra?

Homework Statement Let A be the 4x2 matrix |1/2 -1/2| |1/2 -1/2| |1/2 1/2| |1/2 1/2| Find the projection matrix P that projects vectors in R4 onto R(A) Homework Equations projSx = (x * u)u where S is a vector subspace and x is a vectorThe Attempt at a Solution v1 = (1/2, 1/2...

Can anyone please recommend me a good textbook for Linear Algebra? I want a good textbook for Linear Algebra with lots of practice problems and less theoretical problems. Please tell me the name of the textbook, edition, and author. Thanks.

1. The question is asking: Let V be a 3-dimensional vector space with a chosen basis α = {e1,e2,e3}. Consider the subspace W = span(u,v,w). Represent W as span([u]α, [v]α, [w]α), and then write W as a solution space {X : AX = 0} for some matrix A. 2. u = e1 − e2 + e3 v =...

Hi everybody, I'm a physics student and this is my first post here and i will begin asking one favor: Anyone could recommend a simple and accessible book about vectors in linear algebra?? I'm already read several books and didn't understand anything.. :cry: I really need to recover my...

Homework Statement 2: Some proofs: a) If ##\{ v_1 , v_2...v_n \} ## are linearly independent in a real vector space, so are any subset of them. b) If any subset of vectors ##\{ v_1 , v_2...v_n \} ## in a real vector space are linearly dependent, then the whole set of vectors are linearly...

Given vector spaces V, W, and a function T:V→W , state the two equations that the function T must satisfy to be a linear function. Does T:V→W mean a function that maps vectors in V into W? Or what does this actually mean?

I will start calculus 2 in the fall. I am comfortable with the integration techniques. I did not quite get Taylor series an d the like during self study. I can learn this from the professor swing that I have somewhat completed the cal 2 portion and the semester is 2 months away. now my...

This semester I'm a bit stuck with classes to progress my Electrical Engineering major (having going into it so late), so the only class I can take to progress is a physics course about electricity and the likes. I need at least a three unit class in order to get at least half time so I won't...

Homework Statement Two glasses. First glass has 1 L of water. Second glass has 1 L of alcohol. Step (1) Pour 1/2 of liquids from glass 1 to glass 2. Step (2) Pour 1/2 of liquids from glass 2 to glass 1. What is the limiting situation after 1 billion steps.Homework Equations N/A The Attempt...

I am almost finished with the LA chapter in Mary Boas' "Mathematical Methods in the Physical Sciences",. I love the book so far except for the sections in chapter three that she added in the 2005 edition. They are really difficult for me to unpack all by myself. I need a better reference...

Homework Statement . Let ##A \in \mathbb C^{m\times n}##. Prove that tr##(A^*A)=0## if and only if ##A^*A=0## (here ##0## obviously means the zero matrix). The attempt at a solution. By definition of the trace of a matrix, the implication ← is obvious. I am having problems proving...

This is NOT homework. I am trying to solve a generalized circuit ( each node is a 4-component generalization) and matrices are 4x4 tensors. And I am trying to write them down -- making common nodes "zero" current, ending up with a matrix as in what's shown in the link...

Homework Statement Prove the following theorem: Suppose that B, C, and D are ordered bases for a nontrivial finite dimensional vector space V. let P be the transition matrix from B to C, and let Q be the transition matrix from C to D. Then QP is the transition matrix from B to D...

[FONT=arial]My friend, who is a beginner in college mathematics, recently asked me to teach her linear algebra. She has a good grip on High School math. I am looking for an amusing theorem in linear algebra which can be appreciated by a beginner in college mathematics and at the same time...

Homework Statement Let W be the intersection of the two planes x + y + z = 0 and x - y + z = 0 In R3. Find an equation for Wτ Homework Equations The Attempt at a Solution So, W = {(x, y, z) l 2y =0} I don't think that is a correct was to represent W being...

Homework Statement Let ##V=\mathbb{C}_2## with the standard inner product. Let T be the linear transformation deined by ##T<1,0>=<1,-2>##, ##T<0,1>=<i,-1>##. Find ##T^*<x_1,x_2>##. Homework Equations The Attempt at a Solution Find the matrix of T and then take the conjugate...

Homework Statement The Attempt at a Solution Can someone please check my work?

Could someone help me with this question? Because I'm stuck and have no idea how to solve it & it's due tomorrow :( Let S be the following subset of the vector space P_3 of all real polynomials p of degree at most 3: S={p∈ P_3 p(1)=0, p' (1)=0} where p' is the derivative of p...

I am currently enrolled in Calculus 1. Will be taking Calculus 2 in summer and Calculus 3 in Fall. I have already registered for these courses. One of the Math electives I have a choice in Fall Semester is either Discrete Math or Linear Algebra. Any suggestions would be greatly appreciated...

Homework Statement A is an anti-Hermitian matrix. Show, by diagonalising iA, that: |det(1+A)|^2 >=1 Homework Equations A^H denotes hermitian conjugate of A; A^H = -A\ x = Ox' transforms vector components between 2 basis sets. The Attempt at a Solution I know that iA is a...

Homework Statement If M is a real anti-symmetric n x n matrix, M^2 is a real symmetric matrix. Show that M^2 is a non-positive matrix, i.e. x(transposed) M^2 x <= 0, for all vectors x. Homework Equations det(M) = (-1)^n det (M) The Attempt at a Solution I attempted to use the...

Homework Statement Construct a matrix whose null space consist of all linear combinations of: v1 = (Column matrix) <1 -1 3 2> v2 = (Column matrix) <2 0 -2 4>Homework Equations NS(A) = {x ε Rn I Ax =0} w = k1v1 + k2v2The Attempt at a Solution I'm...

Just came across LU decomposition and I am not sure how to work on this problem: Let L and L1 be invertible lower triangular matrices, and let U and U1 be invertible upper triangular matrices. Show that LU=L1U1 if and only if there exists an invertible diagonal matrix D such that L1=LD and...

Homework Statement Find equation of plan H in R^4 that contains the point P= (2,-1,10,6) and is parallel to plain H2: 4a +4b + 5c-6d = 3 then answer the following questions: A. find normalized normal of plane H which has an angle theta with the normal n= (4,4,5,-6) of H2 such that...

Homework Statement We have seen that the linear transformation ##T(x_1,x_2)=(x_1,0)## on ##\mathcal{R}^2## has the matrix ##A = \left( \begin{smallmatrix} 1&0\\ 0&0 \end{smallmatrix} \right)## with respect to the standard basis. This operator satisfies ##T^2=T##. Prove that if...

Consider the following three vectors in R3: u1=(3,6,2) , u2=(-1,0,1) , u3=(3,λ,7) a) Find all values of λ E R, such that {u1, u2, u3} spans R3, i.e.R3 = span {u1, u2, u3} b) Find the value of λ E R, such that {u1, u2, u3} spans a plane in R3. c) Find all values of k E R, such that the...

Homework Statement Let A be the matrix A = 1 −3 −1 2 0 1 −4 1 1 −4 5 1 2 −5 −6 5 (a) Find basis of the column space. Find the coordinates of the dependent columns relative to this basis. (b) What is the rank of A? (c) Use the calculations in part (a) to...

Hi, I'm reading Shilov's linear algebra and in part 2.44 he talks about linear independent vectors in a subspace L which is a subset of space K( he refers to it as K over L). I don't understand why he says that a linear combination of vectors of the subspace L and vectors of the subspace K...

Homework Statement If dim(X)=n, show that the vector space of k-linear forms on X is of dimension nk.Homework Equations The Attempt at a Solution So I know we need to let x1, x2,...xn be a basis for X. My professor then said to "show that the function fj1,...,jk, 1≤jl≤n defined by...

Homework Statement Let T: C∞(R)→C∞(R) be given by T(f) = f'''' where T sends a function to the fourth derivative. a) Find a basis for the 0-eigenspace. b) Find a basis for the 1-eigenspace. The Attempt at a Solution I just want to verify my thought process for this problem. For...

The time has come to schedule for next semester's classes. I will be a senior in physics and choosing some electives. I am trying to decide between taking matrix theory (linear algebra) or graduate level classical mechanics. I really WANT to take the mechanics course but I feel that maybe I...

Homework Statement Use cofactor expansion to compute determinants of nxn matrices A= (aij)= [0 0 ... 0 1 0 0 ... 2 0 .... 0 (n-1) 0 ... 0 n 0 0 ... 0] B=(bij)= [ 0 1 0 ... 0 0 0 2 ... 0 .... 0 0 0 ... (n-1) n 0 0 ... 0] Homework Equations det(A) =...

Homework Statement Let X1, X2,...,Xn be scalars. Calculate det(A) where A= nxn matrix with [ x1+1 x1+2...x1+n x2+1 x2+2...x2+n ... ... ... xn+1 xn+2...xn+n] Homework Equations det(A) =...

Hi everyone. Long time lurker first time poster. I am taking a linear algebra class this semester and I am really struggling. Does anyone have any good resources for learning/understanding function spaces, polynomial interpolation and orthogonal expansion etc..? Thanks

this probably is a wrong section but i did not know where else to put it (feel free to move it to where it belongs). that said could someone recommend me a pure math linear algebra book? preferably with LOTS and LOTS of examples! i think i have decent grasp of the basic theory but i have been...

We use the term VECTOR in vector algebra, in vector calculus, in Linear Programming and in Linear algebra. For vector algebra and vector calculus, by a VECTOR we mean a quantity having both magnitude and direction. Does it have same meaning in the context of Linear Programming and in Linear...

Are there any Introductory Linear Algebra books out there that are not so proof-laden? All those proofs only make things more complicated and I would rather just learn applications of Linear Algebra rather than sit through a bunch of long proofs. Can anyone suggest some books to me for this...