Column Definition and 317 Threads

Homework Statement In the following exercises verify that the row rank is equal to the column rank by explicitly finding the dimensions of the row space and the column space of the given matrix. A = [1 2 1 ; 2 1 -1] Homework Equations The Attempt at a Solution All i can...

Homework Statement A = [ 1 0 1 -1 1 -3 2 1 0] what is the column space of A? What is the row space of A What is the solution space of A? Also, if i were given a multiple choice, how do I check if a vector is in either the column, row or solution space of A ...

If you have a 3x3 matrix AB of rank 2, and you are asked to find two linearly independent vectors in the column space of A, are those the same vectors in the column space of AB? I figure it is since if the vectors are linearly independent they wouldn't change. Am I right?

Homework Statement the question is in the picture. the rectangular steel bar shown supports a concentric load of 13000lbf. Both ends are fixed. If te modulus of elasticity is 29x10^6 lbf/in^2, what is the maximum length the rod can be without experiencing buckling failure? Homework...

Homework Statement A support column is compressed 2.46 x 10^ -4m under a weight of 5.42 X 10^5N. how much is the column compressed under a weight of 4.8 X10^6N? Homework Equations F=KX The Attempt at a Solution By using that equation, I get 542000 = .000246K Solve for K, and I get a...

Homework Statement Does b = [ 2 15 ]T lie in the column of the matrix A [1 -3] [2 5] Homework Equations a basis of CS(U) forms a basis for the corresponding columns for CS(A) The Attempt at a Solution I reduced the given matrix into row echelon form and determined its column...

Hey fellas could use a hand on a linear question that has been bugging me. Give an example of a 4 x 4 matrix such that col A = nul A Appreciate any help! Thanks, ib

Homework Statement Can anyone help me figure out basis for RS(A) and basis for CS (A) along with their dimension? I mean dim CS(A) and dim RS(A) where A is [1 -2 4 1] [0 7 -15 -4] [0 0 0 0] Homework Equations The Attempt at a Solution are all non zero rows the basis for...

Understading row and column space Homework Statement I am having hard time trying to understand row and column space. Can anyone simplify the meanings of them so that i can visualize them well. Homework Equations dimension of row space = rank ? How? Why? The Attempt at a Solution...

Homework Statement A cylindrically symmetric plasma column in a uniform B field (= B0 in z direction) has n(r) = n0 exp[-(r/r0)^2] and ni = ne = n0exp[e phi/kb Te] where phi is the potential and Te is the temp of the electrons. (a) Show that Ve and VDe are equal and opposite Homework...

A column AB is anchored to the ground by a pin-joint at A, and is held in a vertical position by various loads as shown. Determine: (i) Magnitude of force f1 (ii) Magnitude and direction of the reaction at A I know how to calculate F1 if it was on a horizontal or vertical. But I'm not sure...

Homework Statement At sea level, the pressure of the standard terrestrial atmosphere will support a column of mercury of density 1.359 x 10^4 kg/m^3 and of height 0.7600m at a place where the acceleration due to gravity is 9.80665 m/s^2. Show that 1 atmosphere = 760 mm Hg = 1013hPa. I...

In many problems , to change the length of the air column we use water but I don't understand why waves don't pass into water and then the reflected wave will have less amplitude and hence standing waves could not be formed.

Column Vectors? Alrighty. I have a silly question about column Vectors. I first learned about the concept of a vector in Physics, i.e. position, velocity, acceleration, etc. so I easily understand the premise of a row vector. For example the matrix \left[\begin{array}{ccc}1 & 2 &...

Hi all, I have a class file template which uses double columns throughout. I wish to insert a table which will fill the entire page so I need to somehow break the two column format for a small section and then go back to it afterwards. Does anyone know how to do this? Thanks in...

Hello, just started a LA course, and I have a small question. If I get a zero column while solving for a system of linear equations, and that column corresponds to, say, variable x_{5}, do we just not include it in the solution set since it appears in no equation of the system? Or is it a free...

Hello there, For the following problem, I am arriving at an answer different from the given one so I would appreciate any help or hints. Thank you. My work is shown below. --- 1. A slightly smaller plastic pipe is inserted inside a second plastic pipe to produce an air column, open at both...

resonance in closed air column Homework Statement we have conduct a lab to determine the speed of sound and estimate room temprature by using open air column method. put a tube in the water, have a tuning folks (sound source) on the above, and pull the tube up and down to find the resonance...

Homework Statement If col (A) is column space of A and ker(A) null space of A with ker(A) = {Ax = 0} and ker(A') = {A'y = 0} Homework Equations Consider the (3x2) matrix : A = [1,2 ; 3,4 ; 5,6] (matlab syntax) Show that col(A) = c1 * [1,0,-1]' + c2 * [0,1,2]' The Attempt...

1. Homework Statement [/b] For each of the following choices of A and b, determine if b is the column space of A and state whether the system Ax=b is consistent A is a 2 by 2 matrix , or A=(1,2,2,4) , 1 and 2 being on the first row and 2 and 4 on the second row. and b=[4,8] 4 being on...

Homework Statement In how many ways can eight identical rooks be placed on an ordinary 8x8 chessboard so that no two are in the same row or column? In how many ways, if each rook has a different color? Homework Equations I looked at the equation n choose k (nck), but I don't know if...

[SOLVED] Dimension of column- and rowspace Homework Statement My book doesn't answer this question clearly, but I have notived the following connection: Does the dimension of the rowspace of a matrix equal the dimension of the columnspace of a matrix which equals the rank of the matrix?

I want to know where to look for information relating to toppling. I have looked at stability of equilibrium but the real question is: If say for arguments sake, there is a column 2m high and 1/4m wide - it would be easy, if we knew the weight of the column, to establish the force required...

Hi All, I need to multiply column and row vectors but not sure that I am doing this right (on the picture below): http://img244.imageshack.us/img244/6222/35459606ye4.th.jpg Could you check it and correct if necessary? Thank you.

[SOLVED] Column space, matrix Homework Statement I have a linear transformation f from R^4 -> R^4 given by a matrix. I have to find the range of f(R^4) which containts the vector (x,y,z,w)^T. The Attempt at a Solution I know that the range of f is the column space, how do I make sure that...

Homework Statement I have a linear transformation T which is associated with a matrix A. I want to find the image of T, which is given by the column space of A. I have done this. Now I have a vector B = (x,y,z,w)^T, and I want the vector B to be part of the image of T. To do this, I write...

Homework Statement Find the second resonant length of an air column that resonates with a sound of frequency 1.0 kHz at 15.0 degrees Celsius under each of the following conditions. a) the air column is closed at both ends b) the air column is open at both ends Homework Equations...

I just wanted to know that the following statement is always true or not. After I expand the determinant I get the value of the determinant as zero, ie. I know that the value of the determinant zero. Then with the help of row or column transformations can we transform the determinant into...

Homework Statement A marble column of cross-sectional area 1.7 m2 supports a mass of 30,000 kg. (a) What is the stress within the column? (b) What is the strain? Elastic modulus for marble E (N/m^2) 50e9 shear modulus (G) Homework Equations a)stress=F/A=N/m^2 b) don't know...

Homework Statement What is the weight of a column of water 7 ft high with a radius of 1.1m? The density of the water is 1000 kg/m/m/m Answer in units of N.Homework Equations Volume = pi * r^2 * h 7 ft = 2.1336 m Weight = Volume * Density The Attempt at a Solution Volume = 3.14 * 1.1^2 *...

Hi, I'm new here, so I don't really know how this works, but if someone could help me solve this physics problem, that would be great! An air column open at both ends, has a fundamental frequency of 2000 Hz. What are the frequencies of the first two overtones? I have been stuck on...

How far will a column of a fluid with density p1 fall if it is inside of a tube (open to atmosphere at the top), inwhich the tube is inside of a tank of another fluid with density p2 (p1 >> p2)? Assuming that the tube was intially plugged at the bottom while filling it with the higher density...

Homework Statement A 50-cm-long wire with a mass of 1.0 g and a tension of 440 N passes across the open end of an open-closed tube of air. The wire, which is fixed at both ends, is bowed at the center so as to vibrate at its fundamental frequency and generate a sound wave. Then the tube...

How would I prove this theorem: "The column space of an m x n matrix A is a subspace of R^m" by using this definition: A subspace of a vector space V is a subset H of V that has three properties: a) the zero vector of V is in H. b) H is closed under vector addition. c) H is closed under...

If you were to design a distil col and didn't know the feed conditions how would you go about starting. You know xd, xb, xf, R, Eq data. Theres 5 potential q's. Also how would u make enthpy diagram for PS. Thanks.

1) True or False? If true, prove it. If false, prove that it is false or give a counterexample. 1a) If A is m x n, then A and (A^T)(A) have the same rank. 1b) Let A be m x n and X E R^n. If X E null [(A^T)(A)], then AX is in both col(A) and null(A^T). [I believe it's true that AX is in...

Homework Statement I feel like I'm doing something seriously wrong here.:rolleyes: How tall must a column of water be to generate a pressure of 100mmHg? Homework Equations P = pgh, I think, is the only necessary equation. The Attempt at a Solution So... 100mmHg = 1 kg/m3 * 9.81...

I just need a hint. Problem: find an orthonormal set q1, q2, q3 for which q1, q2 span the column space of A, where A = [1 1] [2 -1] [-2 4] of course I should apply the Gram-Schmidt method, but the problem is that the column vectors are not independent and Gram-Schmidt starts with...

Homework Statement In the experiment of the determination of the speed of sound in air using the resonance column method the length of the air column that resonantes in the fundamental mode with a tuning fork is 0.1m. When this length is changed to 0.35m, the same tuning fork resonates with...

How do you size a packed column with molecular sieves?:confused: Thanks.

A concrete column has a diameter of 350mm and a length of 2m. If the density (mass/volume) of concrete is 2.45\frac{Mg}{m^3}. determine the weight of the column in pounds The answer to this problem is given as 1.04 kip not pounds like the question ask for, but that is not my problem. This...

Homework Statement What is the shortest air column, closed at one end, that will resonate at a frequency of 440Hz, when the speed of sound of 352m/s Homework Equations the patterns The Attempt at a Solution ive tried

Homework Statement Show that if the vector \textbf{v}_1 is a unit vector (presumably in \Re^n) then we can find an orthogonal matrix \textit{A} that has as its first column the vector \textbf{v}_1. The Attempt at a Solution This seems to be trivially easy. Suppose we have a basis \beta for...

Many university organic course laboratories use Liebig columns packed with glass beads. This is what I use, but I would like to know if there are better columns that can be used instead of this. I had a problem with this type of apparatuse before. The glass beads shot right through the $30...

Hey, I was looking for help on these questions dealing with row and column spaces... 1. Prove that the linear system Ax = b is consistent IFF the rank of (A|b) equals the rank of A. 2. Show that if A and B are nxn matrices, and N(A-B) = R^n, then A = B The first one I can't get much...

so i tried looking it up on various sources including wikipedia, and i am still confused about column space actually is. maybe it would help if one of you explained it to me?

A straight conical column made of steal (original length 1000mm, head diameter 90 mm, ground diameter 190 mm) is loaded by a normal force F = 1450 kN. What is the length under load ? for this ,the diameter is changing along the column,should i assume is as hollow and use the hollow formula...

What is the pressure of a 10 cm high column of mercury (ρ = 13,6 g/cm^3) in hPa? i know that the formula is Pressure=pgh so i subs in 13.6g/cm^3 (9.81m/s^2) (10cm). may i know what is the g in 13.6g/cm^3 belongs to?? is it equals to 9.81m/s^2?? and also what is hPa??i know Pa is pascal...

Sir, Consider a resonance column which is in unison with a tuning fork of particular frequency. Now by varying the length of the air column, resonance is obtained at different lengths. How is this possible? I have this doubt because each length of air column vibrates with a particular...

Here's the situation: you have a pipe in a bucket of water and can vary the length of the air column in the pipe by raising or lowering it. Here's my question, hope someone can help. The speed of sound in helium is three times greater than the speed of sound in air (340m/s). Under these...