Column Definition and 317 Threads

Homework Statement Suppose that A and B are 5 x 5 matrices with the same Column Space (image). (a) Must they have the same columns? (b) Must they have the same rank? (c) Must they have kernels of the same dimension? (d) Must they have the same kernel? (e) If A is invertible, must B be...

Homework Statement What is a pivot column?Homework Equations The Attempt at a Solution I tried google for some examples but I cannot find any. I need to know what exactly a pivot column is because I am trying to do a Linear Algebra problem about consistency and inconsistency. Can anyone...

Hi, I have put my data in column form ( a large number of data) in Notepad. I have attached example of the data. I know how to import it into Mathematica. However I face the problem to change the whole set of data to row form in Mathematica so that I can plot the histogram in Mathematica. Thanks.

What's the "column effect"? Reading about trusses, it says I'm not sure what's the "column effect". There's no wiki entry and Google seems to show me many results that don't provide the definition...

Homework Statement If we let A be the augmented m x (n + 1) matrix of a system of m linear equations with n unknowns Let B be the m x n matrix obtained from A by removing the last column. Let C be the matrix in row reduced form obtained from A by elementary row operations...

Equivalent length of of column ?? Homework Statement A Mild steel column has a cross section of 100 mm by 50 mm . Assuming a safety factor of 6 calculate the load that it can safely support? Homework Equations Rankines formula : W = Oc/K[1+a(AEe^2/I] The Attempt at a Solution...

Homework Statement OMG, Embarrassing typo ^ *HEAT not HEART. :) Sorry! In any case, A construction worker uses a steel tape to measure the length of an aluminum support column. If the measured length is 18.6 m when the temperature is 21.2 C, what ist he length when the temperature rises to...

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...

I was wondering the critical load vary as a result of forced vibration? Intuitionally, I thought the critical load reduced. But how to show it analytically, Any idea?

Homework Statement This question is a product of my own mind- Refer Figure. Suppose the value of P= 2Patm, can 2Patm fall to Patm before the liquid levels with the hole-level? In other words, can there be a liquid column above the hole?

My problem is proving my structure is sound. Currently i want to know my deflection from my loads applied. See attachment. My load is 4000 lb. My carriage weight is 1200 lb. My upright column or tube is a 6" x 4" x 1/4" structural steel which i have 2 of these. I have distances to my CoG...

I'm trying to figure out how to set up a matrix where I don't know the last value ex a+2+4=x, b+4+6=x, c+2+6=x. Would it be something like this? [1,0,0,x-6] [0,1,0,x-10] [0,0,1,x-8]

Yet another silly question from me :/. From an instructor's notes: "Let V = R^n be the vector space of column n-tuples of real numbers." Not quite sure what the "tuple" means. For R^3, would an example be the transpose of (1,2,3)? Thanks in advance for responding. While we're at it, any...

Am I missing something and doing this all wrong? Experiment and data: The level of water in the glass tube was adjusted by raising the supply tank until the sound from the tuning fork was at its loudest. This level corresponds to first resonance position and it was recorded. The...

Homework Statement This is for a lab I finished but cannot get this question, I spoke with the TA today and she made it make sense but I am still not getting the question correct. (2) The difference in pressure between the lowest and the highest measurement point is related to the weight of...

Homework Statement The U-shaped tube in the figure has a total length of 1.0 m. It is open at one end, closed at the other, and is initially filled with air at 20C and 1.0 atm pressure. Mercury is poured slowly into the open end without letting any air escape, thus compressing the air. This is...

When we calculate the stresses in the section of a Reinforced Concrete column reinfored with Steel Rods, it is seen that the percentage Load carried by the Steel is much greater than the percentage area it contributes in the cross sectional area of the reinforced concrete section. The load...

hi, can anyone help me with the formula for a vertical Column (C-Channel) subjected to Eccentric Loading? Regards, Subbby

Homework Statement Consider the matrix A: 1 4 5 0 9 3 -2 1 0 -1 -1 0 -1 0 -1 2 3 5 1 8 (Sorry I don't know how to do TeX matrices on this site) Find a basis for the row, column, and null space. Homework Equations The Attempt at a Solution I reduced to row echelon form, which...

[b]1. You perform an experiment with a long column of air and a tuning fork. The column of air is defined by a very long vertical plastic tube with a circular cross section; the upper end of the tube is open to the outside air and the lower end of the tube is filled with water. The column of air...

This may seem like a very obvious question, but I thought it may be some sort of trick that my lecturer thought I may overlook... Well, when swapping columns of an augmented matrix, the solution set is unchanged (as long as you don't swap the 'b' column) is this correct? It is only swapping the...

Hi, Thank you for taking the time to look at my problem. I am considering a vertical pole fixed in the ground at the bottom and experiencing a horizontal point load at the top. This pole is fixed with guy ropes from the top to the ground at a certain angle. See attached image. Assuming...

X is a 10x10 matrix what is X*[7th column of X's inverse]? thanks for any help you can provide!

Homework Statement I thought that if you have a square matrix then the column space is the set of all linear independent vectors which can be written as a linear combinations of the others? Which inturn is the same as range of the Matrix? Am I wrong?

Homework Statement The density of air in the lower atmosphere decreases exponentially with height: ρ = ρ0e−z/H where ρ0 = 1.3 kg/m3 and H = 10 km. What is the mass of air in a cylindrical column of cross-sectional area 1 m2 and height z, as a function of z? How much mass is contained in such...

Knowing that the torsional spring is of constant K and that the rigid bar is of length L, determine the critical load P_{cr} beyond which the column would buckle. See pic for the problem. [As the spring uncurls, it applies moment K \theta to the bar.] The answer is P_{cr}=K/L

I have a problem with a constrained column under thermal stress where I am to find the reaction forces at the supporting ends of the column due to its own weight after being heated. Attached is the problem, equations used, and my solution attempt. I tried to solve for the reaction forces...

Hi there I'm a complete novice about this kind of thing, but I've decided to fulfil a long dream of mine and make a bookcase with a secret door in it :) I've thought about various methods, but eventually I've figured that the best system would be to make it rotate around a spindle on one...

Can anyoune tell me how you flip a column in origin so you are reading it from bottom to top? I don't mind if it means making a new column. Or if this isn't possible then is it possible to do a differential when taking the bottom values first?? If that makes any sense Thanks

Hello, Suppose that \mathbf{h} is an N\times 1 column vector. Can we say that: \mathbf{h}^*\mathbf{h}=\mathbf{h}\mathbf{h}^* where * means complex conjugate transpose? Thanks in advance

Ok folks i thought i would use this forum for once. if i have a 2 foo by 2 foot by 10 foot long metal column and a perfect level floor, and place the column on end so it is 10 feet tall it should be pretty straight and square to the " perfect flat and level floor " surface..right! assume the...

Let A_i (i=1,...,k) be a nonsingular complex matrix which size is M by M. The question is how to find a complex matrix X which size is M by N such that: span(A_1*X)=...=span(A_k*X) (I guess that there must be relations between M,N and k when nontrival solution exists. ) ask: 1)if non...

Homework Statement Ax=b where, A = 1 -1 ...-1 1 Homework Equations a) Find Null Space N(A) and Column Space C(A) b) For which vectors b does the system Kx=b have a solution? c) How many solution x does the system have for any given b The Attempt at a Solution a) For Null Space, I got x =...

Homework Statement Ax=b where, A = 2 -1 ...-1 2 Homework Equations a) Find Null Space N(A) and Column Space C(A) b) For which vectors b does the system Kx=b have a solution? c) How many solution x does the system have for any given b? The Attempt at a Solution a) For Null Space, I...

Homework Statement As quoted from the question sheet: When building a tall support, often the self weight of the support must be considered. For an optimal support, the volume of material, and hence the cost, will be a minimum. If the maximum allowable stress in concrete is 12 MPa, determine...

For the two matrices A and B, (AB)i,j = ri [SIZE="4"]. dj ---- [SIZE="4"]. refers to dot product ---- ri is the ith row in A and dj is the jth column in B. Let us say that A and B are n x n system of column vectors. Then a row vector ri of A would correlate to a component vector of the sum of...

Homework Statement Why does no 3 by 3 matrix have a nullspace that equals its column space? Homework Equations NA The Attempt at a Solution A = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix} \] C(A) = \begin{bmatrix} 1 \\ 0 \\ 0...

Arrange the nine cells of a 3x3 square with digits from 1 to 9, with each digit occurring exactly once, such that: ## The respective totals of the first column, second column and the third column are 15, 19 and 11, and: ## The respective totals of the first row, second row and the...

To find the column space of a matrix, you reduce the matrix and those columns that contains leading variables(pivot columns), refers to the columns in the original matrix who span the columnspace of the matrix. But does the pivotcolumns in the reduced matrix also span the column space of the...

Given an n x m matrix, in which there is a column of 0's or a row of 0's, would it be equivalent to write the matrix while neglecting the column or row of 0's?

Homework Statement A closed air column is 60.0cm long. Calculate the frequency of the forks that will cause resonance at: a) the first resonant length b) the second resonant length Note that the speed of sound is 344m/s. Homework Equations Ln = (2n - 1) * \lambda / 4 fn =...

a steel bar 1 " sauare 6 ' long is to be used as a column.ends are free to rotate put may not be displaced stress is limited to 30,000 psi. i believe my teacher expect conform code AISC.

Having much difficulty with the problem below. Any direction would be greatly appreciated. A waste gas stream contains .045 mole of ammonia per mole of carrier gas. Its desired to design an absorber using water which will reduce the ammonia concentration in the exit gas from the absorber to a...

Homework Statement Given matrices A and B, show that the row vectors of AB are in the row space of B an the column vectors of AB are in the column space of A Homework Equations Just matrix multiplication, reduced row echelon form, and leading one's for row and columns The Attempt at...

Hello, I'm new to Latex and I'm having some problems creating a 5 x 5 matrix. I need to label each column 1 through 5 and I need to label each row 1 through 5. I need the row labels to be on the right side. I've found a couple of links online, but they only show how to label rows on the left...

Homework Statement Solve the matrix equation: [10 1 9 1 4 3 2 -1 3] X = 3X where X is a column matrix. Please show all the steps, thanks. The Attempt at a Solution I think the solution is X = kU, where k is any constant and U is the vector... yet not really sure how to...

Hi, I was running a labview program and it wrote my data to an lvm file, which can be opened with notepad. The problem I am having is the way labview outputted my data. It has the time and the strain separated by a comma. I attached the file, so everyone can see. What I want to do is somehow...

Homework Statement We have a matrix A which row-reduces to: A = \left[\begin{array}{ccccc} 1&2&0&0\\ 0&0&1&0\\0&0&0&1 \end{array}\right] I'm asked to find the column space of A. Homework Equations The Attempt at a Solution I'm not sure what to write down for this...

Homework Statement A 1.0m long vertical tube is filled with water. A tuning fork vibrating at 580Hz is held over the open top of the tube as the water is slowly drained from the bottom. At what water heights, measured from the bottom of the tube, will there be a standing wave in the tube...

I am just wondering what is meant when someone says the Col A is a subspace of null Space of A. What can you infer from that? Also what is a null space of A(transpose)A How do they relate to A? Are there theorems about this that I can look up?