Column Definition and 317 Threads

I see that the pivots in columns 1 and 2 help us decide which columns to take. But why does the L matrix of this B = LU let just to read off the column space? 2:18

Hey, let's say that in 2D space we have a 2x2 rotation matrix R. Normally you could multiply this rotation matrix by a 2x1 column matrix / vector X. In that case it would be XR to get the vector rotated in the way described by R. Now what I'm wondering is, what if I had 3 column vectors that I...

i need to create a function that returns the pure zeros on the left semiplane and 0 if there is one and only one zero in the origin of the referential. the return has to be in a column vector like [root1;root2;...;rootn;0] or [root1;root2;...;rootn] if there is no root in the origin of the...

Say a subspace S of R^3 is spanned by a basis = <(-1,2,5),(3,0,3),(5,1,8)> By putting these vectors into a matrix and reducing it to rref, a basis for the row space can be found as <(1,-2,-5),(0,1,3)>. Furthermore, the book goes on to say that this basis spans the subspace S. Cool, not...

Homework Statement [/B] This is a seemingly simple problem. All I have to do is multiply two matrices: [ 1 0 ] [ 0 1 ] (A) and [ 2 ] [ 3 ] (B) The Attempt at a Solution [/B] Because the matrix A has the same number of columns as matrix B has rows, and because matrix A is an identity matrix...

How would you prove that adding two vectors in the column space would result in another vector in the column space? I know this is maybe the most basic property of vectors and subspaces, and that the very definition of the column space says it's spanned by vectors in the column space. Is there...

Hey PF, I'm having trouble seeing the bigger picture here. Take matrix A and matrix B. If B can be obtained from A by elementary row operations then the two matrices are row equivalent. The only explanation my book gives is that since B was obtained by elementary row operations, (scalar...

Any1 can explain in an easy way?I know is something to do with the facts that row operations do not change the determinant of a matrix and also determinant of A=determinant of A transpose.But just dk how to prove in full sentence. Appreciate any1 help.

What's the way to convert n(r) to \rho(r) in case of a spherical cloud. n(r) is the column density, \rho(r) is the density. I tried (but didn't manage) to get it from their relation to the total mass: M = 4 \pi \int r^2 \rho(r)dr = 2 \pi \int r n(r)dr (is it correct anyway?) Thank you,

Homework Statement A column of dry air, of cross-sectional area 1m2, has a surface pressure of 1atm. Over the course of several hours during the day it gains 2MJ of energy from radiation and surface heating. There are no horizontal exchanges of energy of mass, and it remains in hydrostatic...

Why it is important to know about Column space and Null spaces in Linear Algebra?

I've made a program with Mathematica that will compute the load along with the moments sustained by a concrete column given the stress block area and orientation(in other word the neutral axis center location and the angle it makes with the horizontal). However I am facing an issue with setting...

Question on Energy conservation -- Car pushing on air column Homework Statement An automobile moving through the air causes the air velocity to decrease and fill a larger flow channel. An automobile has an effective flow channel area of 3 m^2. THe car is traveling at 90 k/h on a day when the...

Homework Statement Here is the problem with the solution: I feel like the solution should be 10.74m. The maximum allowable length should be the lower one. This is because, for example, if we make the column 11m in length. The Pcr in the zy plane would decrease and since we are applying...

i thought if A is 3x5, the columns of A must be linearly dependent, since the rank is at most 3, and the rank is the number of linearly independent columns in A. but there are 5 columns in A, so the columns of A must be linearly dependent :/

Homework Statement There is a cylindrical vessel of cross-sectional area 20cm^2 and length 1m is initially filled with water to a certain height as shown. There is a very small pinhole of cross-sectional area 0.01cm^2 at the bottom of the cylinder which is initially plugged with a pin cork...

So apparently the natural frequency is zero for uniform column with axial load when P is equal to the critical buckling load. Could anyone please explain theoretically why this is the case.

The apparatus looks like this (see attached): I understand that in order to resonane with the tuning fork the air inside the column must be vibrating at the same frequency as the fork. In addition, I understand that varying the amount of water in the tube increases or decreases 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...

Dear all, I am currently doing a lab question. I do not know how to solve a calculation question. Question: Calculate the average flux of the oxygen through the gas-liquid interface in the wetted-wall column. Remember that a more accurate value of the average flux can be calculated by...

I want to show a vector in matrix but I didnt uderstand differentes between row matrix and column matrix Let's suppose I have a 2i+3j How I will show this vector in matrix ? I will use a row matrix or column matrix.

Homework Statement We place a speaker near the top of a drinking glass. The speaker emits sound waves with a frequency of 3.75 kHz. The glass is 14.1 cm deep. As I pour water into the glass, I find that at certain levels the sound is enhanced due to the excitation of standing sound waves in...

Good afternoon, I have created a column vector with many values however I want to know a specific value found in that vector. Specifically I want to know the 99th value of my column vector. Is there a command I can enter into mat lab that will give me the value I seek without having to...

Homework Statement A clarinet behaves as an air column that is open at one end. For a particular fingering, the length of this air column is 24.6 cm. At 20°C, this fingering sounds the pitch "F" which is 349.2 Hz. During a concert, the breath of the musician raises the bore temperature to...

Hey guys, I have a problem where I am supposed to prove that R is nonsingular iff A is of full column rank in a QR decomposition. I feel like I fully understand the two major processes for obtaining a QR decomposition (Gram-Schimdt and Householder Transformations), however, I am not entirely...

I have a data file, let's say test.dat which is contain [1 2 3 4 5 6 7...3000]. the question is how can I re-arrange this data from a row into a column so that I will have a set of data like this 1 2 3 4 5 6 7 . . . 3000 in fortran90 or MATLAB also will be okay. thank you

Fill in the F column values in the truth table for the circuit. Need someone to check my work. My Answer: x y z | f | x! and y! | x! XOR z| 0 0 0| 0 | 1 | 1 0 0 1| 1 | 1 | 0 0 1 0| 1 | 0 | 1 0 1 1| 0 | 0 | 0 1 0 0| 0 | 0 | 0 1 0 1| 1 |...

On Earth. Theoretical study. With a perfect liquid (no viscosity). A bubble in a column of liquid is moving up, the column is on a table, I have some questions: 1/ the force on the table increase/decrease when bubble is moving up ? 2/ the center of gravity of {column+liquid} is always the same...

How to pull up the water which is 800 feet below the ground? How much amount of pressure to be applied ? Can we use P = dghReply me as early as possible?

Hi everybody, I need assistance. I have excel file that conntains a date column and another column. I wish to plot the date on x-axis and the second column on y axis. I wrote the MATLAB code below. This is my code. data=xlsread('DataTest','Sheet1'); q=data(:,2); time=data(:,1); Error...

Hello! The following system of linear equations has been expressed in term of column vector in the following. . How can I express the system of linear equations in term of row vector? In addition, What is the field of scalars? I would request to explain it. Thanks in advance.

If u=(3, 3 , 3) is a vector in R3 then we can draw the vector in a three dimensional space.(3=x coordinate, 3= y coordinate, 3= z coordinate.) if x = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_m \end{bmatrix} is a column vector in Rm then how can we draw it? In addition we call X =...

We know that we get first resonance when the length of the air column is λ/4. We get second resonance when the length of the air column is 3λ/4. This is because we get a node at the surface of the water after λ/4 distance in the first case and 3λ/4 in the second case. My question is that what...

Homework Statement Column supports a mass on its' top. So force is downwards. Column properties: Do = 50mm (outer dia) Di = 40mm (inner dia) E = 250 GNm^-2 (modulus of elasticity) V = 0.33 (Poissons ratio) Homework Equations Poissons ratio = Transverse strain = - εt / εl Transverse strain...

In my linear algebra class we previously studied how to find a basis and I had no issues with that. Now we are studying the basis of a row space and basis of a column space and I'm struggling to understand the methods being used in the textbook. The textbook uses different methods to find these...

It ran in Science News after much calculation the idea shape for a column to resist buckling was solved. It is a slight barrel shape.

Hello, I have the following Latex code, and I need to draw an arrow that connect each column by the corresponding entry in the last (separated) row, e.g.: the column [x_0^{(1)} x_0^{(2)} ... x_0^{(M)}]^T with the entry x_0^{(R)} and so on. How can I do that? \documentclass{article}...

Homework Statement A solid cubical block with a side of 11.0 cm floats in mercury so that 5.48 cm of the side of the block is submerged in the mercury. Water is then poured on the system until the block floats completely submerged. calculate the height of the water column that was added. The...

I have a program that makes a histogram from data taken in a file but it only works if the data is an array (nx1 matrix). I've downloaded a data file which is a 159663x12 matrix but only the 8th column contains numbers I'm interested it. The other columns contain either letters and/or numbers...

Hello! I got a problem wrong and I'm trying to figure out what happened. it's triangle ABC bisected by line BD Given line BD is the perpendicular bisector of line AC, Prove line BD bisects angle ABC I got Step 1 Line BD is the perpendicular bisector of line AC Reason: Given Step 2 Line D is...

Jorrie obviously doesn't have to adopt any of our suggestions in building his tabular (cosmic history) calculator. It's his project and he's doing all the work. But he's said in several threads that he would like reactions/suggestions from us (and he may have used them in some cases.) Maybe...

Positive real numbers are arranged in the form: $$1 \;\;\; 3 \;\;\; 6 \;\;\;10 \;\;\; \cdots$$ $$2 \;\;\;5 \;\;\;9 \;\;\; \cdots$$ $$4 \;\;\;8 \;\;\; \cdots$$ $$7 \;\;\; \cdots$$ Find the number of the line and column where the number 2002 stays.

Homework Statement For a solar tower compare the total force on the air column in the tower (i) by calculating the pressure at its bottom and top (ii) from Archimedes’ Law. Hint: there is a temperature difference between top and bottom of the tower. I have to estimate height...

Hey I have a text file with 2 blocks of Data Example Numbers 1: 1,2,3,4,5,6 7,8,9,10,11 ... Numbers 2: 92,93,94,95,96 97,98,99,100,101 ... How would i use FORTRAN to read the text file and output in a column and row format.. Example 1 92 2...

Homework Statement Given a matrix A. So I can reduce A to ref(A). Let's say in ref(A), the columns that contain leading ones are column 1, 3, and 5. True or false: (a) Columns 1, 3, and 5 from ref(A) form the column space of ref(A). (b) The corresponding column 1, 3, and 5 from the original...

Homework Statement I'm given a 4x5 matrix with one missing column. I'm also given the RREF form with no missing columns. Previous parts of the question made me find the row, column, and null basis for the matrix. Now it's asking: d) Find the missing column. (Hint: Are the columns of...

Hi We have a matrix A (picture), the eigenvalues are λ1 = 4 and λ2 = 1 and the eigenvectors are λ1 : t(1,0,1) λ2 : t1(1,0,2) + t2(0,1,0) I have to examine if there's a column vector v that satifies : A*v = 2 v I would say no there doesn't exist such a column vector v because 2 isn't an...

Question 7c on attached, in the solutions could someone explain why the person multiplied the column vector OB by h? I don't get it

1.Construct a matrix whose null space consists of all linear combination of the vectors, v1={1;-1;3;2} and v2={2,0,-2,4} (v1,v2 are column vector).2.The equation x1+x2+x3=1 can be viewed as a linear system of one equation in three unknowns. Express its general solution as a particular solution...

In this theorem it states " Let A be a m x n matrix. That is For each vector b in R^m, the column Ax=b has a solution..." Why do they say that bεR^m? Is that because b is a mx1 column matrix where it has m rows making it belong to R^m?