Columns Definition and 106 Threads

Why is it not possible for the columns of a matrix to span R^2 even if those columns do not span R^3?

Hi everyone! I was reading up on sound waves and I got to the point where this website was describing how instruments produce standing waves through the interference of different frequencies but then it started to talk about how the length of air columns can affect the wavelengths of the sound...

Ok i have a question regarding columns and it goes a bit like this, What is the minimum length of the column at which buckling is likely to occur? They have given me the youngs modulus of 200GNm-2 (200,000,000,000 Nm) and a yield stress of 140MNm-2 (140,000,000Nm). For working out my...

As the title says, how can I put my matrices in columns in Latex? Say I had two matrices, \[ \left( \begin{array}{ccc}a & b & c \\ d & e & f \\ g & h & i \end{array} \right) \] and \[ \left( \begin{array}{ccc}j & k & l \\ m & n & o \\ p & q & r \end{array} \right) \] then how can I get them...

Hi everyone, This not a homework question. I'm reviewing some linear algebra and I found this on a worksheet. I just need a hint on how to approach this problem. Let β=\{ v_1,v_2,...,v_n\} be a basis for R^n . Let M be the matrix whose columns are the basis vectors in β. Do the...

Homework Statement Prove: if (Q^-1)AQ=D, then each column of Q is an eigenvector of A. Homework Equations A vector v is an eigenvector of A iff there exists a scalar λ such that: Av=λv The Attempt at a Solution Suppose (Q^-1)AQ=D. We need to show each column of Q is an...

Hi everybody, I have 3 columns of data (3 different variables) and 400 rows. How would I set up a matrix/array sort of thing to read each row individually and store it in my fortran program to calculate equations at each step? What I have basically tried and can't get to work, I think it...

Homework Statement Given matrix A= 1 1 -2 1 3 2 -1 2 2 6 3 2 -4 -3 -9 x= x1 x2 x3 x4 x5 b = 1 2 3 1. Solve the system by elimination (use the augmented matrix) until pivots are found (no backward elimination here). 2. Show that pivots...

Homework Statement Consider an n x m matrix A with n >= m. If all columns of A are orthonormal, then A'A = I. What can you say about AA'? Where A'A = transpose(A)*A and AA' = A*transpose(A) Homework Equations The Attempt at a Solution For the case that n = m: A is square...

Homework Statement So, I want to find the pivot columns to the matrix A: A= -1 1 -5 0 2 3 0 6 1 -1 2 -1 7 2 1 2 -7 25 5 1 and after that I want to solve Ax = b where b is (I kind of want to solve Ax = 0 as well, but let's skip that...): b= a+3 2a -a-1 -9a-5 My thought was...

Homework Statement A weight (mass given) is sitting on a beam that is supported by two columns. Given the location of the weight on the beam, calculate the force on each column. Homework Equations not sure The Attempt at a Solution not sure

Suppose I have a MxN matrix and each column may contain exactly 1 zero or no zeros. Is there a transformation that when applied to this matrix will return another 1xN matrix with a 0 in the corresponding column if that column in the original matrix contains a 0 or a 1 in the column position...

Hi all. I need more brain power than I can muster. This is a two part question for a software function I need to write. I'm trying to 1) pre-determine how many n% unique ways there are to intermix items from various lists and 2) produce output of only combinations that are n%...

If you had to prove that your method for cleaning chromatography columns works and you had different sizes and shapes of columns, which one would you pick as a worst case to focus on? You have tall, skinny columns and short, fat columns, as well as different sizes. These are cylindrical glass...

What does the term "ground" mean in an ELECTRONIC circuit? A bus strip usually contains two columns: one for GROUND and one for a supply voltage. What does ground mean in this context and how do we ground a circuit while using a breadboard?

Homework Statement Just need help identifying pivots columns \begin{bmatrix} 1 & 1 & 1 &1 &1\\ 0& 0& 0& 0&0\\ 0& 0& 0& 0&9 \end{bmatrix} From my understanding, any column with 1s and everything below it 0s are all pivot columns right? Is the above all pivot columns...

Hi I am a beginner in using Matlab software. I want to combine 300 columns into one matrix. The dimension of each column is 24x1. Meaning, the resultant matrix should have a dimension of 24x300. Anybody can help me in this? Any help is much appreciated! Thanks

I am a bit puzzled by the following. You know how they teach you that in order to find column space you just need to row reduce the matrix, look at the columns with leading 1's in them and then just read off those columns from the original matrix? Well, why does that actually work? I'm trying to...

Homework Statement Hollow tube chimes are made of metal and are open at each end. One chime is 0.54 m long. A) if the speed of sound is 346 m/s, what is the frequency of sound produced by the third resonant length? B)What would happen to the frequency of sound produced by the third...

I am doing research on open air column resonance. In an experiment I suspended copper pipe and struck it with a hammer. I measured the fundamental frequency for many lengths of pipe. After analyzing the data, I was surprised with the relationship. My research indicated that I would use the...

I am fractionally distilling ethanol out of solution. I have done this with a Snyder column (3-ball)and most of my fraction came over between 79°+ and 83°. I am wanting to improve upon this and am thinking about stacking a Vigreux in there. Should the assembly have the Snyder on the...

Hello all, I wrote a C program to multiply a column of numbers (for eg., number will look like this 10.45618) with some constant... after multiplication i get the correct value (i tested using calculator). Now the output is 0.00005672 (i use %14.9lf) ..but i want them to display like this...

Hey I was wondering how you're supposed to calculate the buckling force for a short column. Is there even a way? If there is, is it accurate and how do you use it? And finally how do you know when to use it?

I'm trying to make a table in LaTeX in which all the entries of a column have the same units, without having to type them for each column. (Before you say it, yes, I know I could just put the units in the column heading, but I don't want to). I tried: \documentclass{article}...

Hi, can anyone explain to me if a 3 x 4 matrix can have independent columns? How about independent rows? Thanks!

Homework Statement Let A be an m*p matrix whose columns all add to the same total say "s". Let B be a p*n matrix whose columns alladd to the same total say "t".Prove that the n columns of (AB) all sum to st. Homework Equations This is an obvious result but i am having trouble proving...

I want to create a title that spans the entire width of the page and then below the title, I want the actual text to be in two columns. I am currently using \documentclass[twocolumn]{article}, which puts the entire document into two columns, including the title, which is now in the left column...

Homework Statement Were the columns of A linearly independent? The matrix A is given in row reduced echeleon form 1 2 0 0 0 0 1 0 0 0 0 1 Homework Equations Hint: Consider the solution set to A x = 0 The Attempt at a Solution I think that the...

I have an assignment where we have to use loops to print quarter diamond patterns. I don't really need help with the actual coding, since the prof basically gave us a pseudo-code as a hint, but in the pseudo-code there is a variable for the number of rows and columns. I have been searching...

Homework Statement Determine the constants c_{1},c_{2},c_{3},c_{4} of the column displacement equation where k=\sqrt{\frac{P}{EI}} In lab we subjected 3 specimens to a compressive load in a pinned-pinned and clamped clamped configurations. I have to compare theory results to...

Homework Statement I need to create a function for scilab which adds a row of zeros to the right of an nxn matrix, a. I also have to add a row of 6's at the bottom but I think i have that part down. Homework Equations I think ones(,) is supposed to help? The Attempt at a Solution...

Hello I have a question, I haven't got my books with me.. So hope you can help me.. I have a crane system like this: http://dl.dropbox.com/u/559096/column.jpg If the column have the boundary: Fixed-Free. Is there a easy way to calculate the maximum displacement? (in the top)

Hi, I have a question from an engineering science assignment that I'm stuck on. 1. Select the lightest wide flange section that can be used as a steel column 7 m long tosupport an axial load of 450 kN with a factor of safety of 3. Use 200 MPa as the limit of elasticity, 200 GPa as the...

does anyone know how to copy data from Notepad file [Text Document] into Excel? the data I need to copy is two columns of numbers, but when I copy-paste them they appear as one column, I just couldn’t manage to separate them [they are about 40 pages long:cry:]. anyone have any suggestion, thanks...

Hi all, I need some help. Select the lightest wide flange section that can be used as a steel column 7m long tosupport an axial load of 450kN with a factor of safety of 3. Use 200MPa as the limitof elasticity, 200GPa as the modulus of elasticity and assume that the column issimply...

If Q is an m x n (m > n) matrix with orthonormal columns, we know that Q^TQ = I of dimension n x n. I have a question about QQ^T. It is a symmetric m x m matrix but also appears to be singular. Why would it be singular? Probably something basic I've long since forgotten.

Ok from other posts, everyone seems to say that it doesn't matter if you stick vectors into a matrix via columns or rows. So i want to prove this to myself using an example from my notes. The only problem is, I get different answers. Can someone correct me? from my notes it says "show (0...

is is based on the experiment where we had to find the point in which tuning fork forces air inside open-ended air column into resonance, the length of the tube is altered by changing the water level in the tube. the water level can be altered by raising or lowering a reservoir of water, thus...

Homework Statement Let a_1,...,a_n be Real. Then define a 2n x 2n matrix A as follows. The following are the first 4 and the last 2 columns; note that the (2k) column equals (a_k)(derivative of the (2k-1) column A[,1] = a_1^(2n),a_1^(2n-1),a_1^(2n-2),...,a_1^(2), a_1 A[,2] =...

Homework Statement An air column closed at one end has a fundamental frequency of 500Hz. What are the frequencies of the first two overtones? Answers: 1500Hz 2500HzHomework Equations Overtone: f = (n+1)f n = overtone Harmonic: f = nf The Attempt at a Solution f1 = (n+1)f = (1+1)500 = 1000Hz...

Homework Statement Let M be an n x n matrix. Prove that the columns of M form an orthonormal set if and only if M-1 = MT. The attempt at a solution Let's consider the following 2 x 2 matrix \begin{pmatrix} a & b \\ c & d \end{pmatrix} If the inverse equals its transpose, i.e...

Hi wondering if can anyone help me... I've gotten so bogged down in all the rules and stuff for singular/non-singular matrices I've completely confused myself! Can anyone tell me is it true to say that if I have a matrix P, det(P) is NOT EQUAL to 0, then the vectors that would form the...

Hi, I got one table of four columns. e.g. Temperature, Field, Vhall and Vdrive. Table contains the 1000 rows. I am given the Vhall_maesured and Vdrive_measured values. I want to find out, which row in the table has the closest values for Vhall and Vdrive to corresponding...

Hi, I've posted another thread asking for general help on how to solve numerically with excel. Here is my specific situation if anybody is well versed with Mathematica programming. I'd appreciate any help. I've successfully created a FindRoot to solve eqn's for one set of data points...

C++ program--help printing columns and rows Homework Statement Print the approx of e^x from 1 to 100. It might not fit on screen so for example print out in 10 columns and 10 rows.Homework Equations int row =1; while (row < 20) { int column = 1...

Homework Statement The question I'm working on is First the diagram:http://http://i215.photobucket.com/albums/cc10/Spookie71/image0-12.jpg There is the matter of the equation I use to solve the equation: Can you please explain for me? Scott

my group was designing an experiment for class where we have to find a length of a column, we started with open, to match a frequency we wanted. we started out with straws, and extended straws, to using the straw as a reed and blowing into a pvc pipe. nothing has worked, our frequency arent what...

Homework Statement Are the columns of this matrix linearly independent? 1...3...-2 0...-8...11 0...0...1 0... 0... 0 (periods are just to make spacing clear) The Attempt at a Solution What is confusing me is the last row of zeros. If a set of vectors contains the zero vector, it is linearly...

my assignment is as follows: write a programme printing a reasonably sized table of powers, in a nice format. using %nd in printf will write an integer in at least n charcaters. this facilitates printing tables with aligned columns. here's my code: #include <stdio.h> #define STOP 10 int...

Homework Statement The 3rd resonant length of a closed air colum is 75cm. determine the 1st and second length. Homework Equations the rensonant patterns The Attempt at a Solution i just don't get this resonant things.