Row Definition and 220 Threads

Hi, Given an over-determined system of linear equations y=A c, the condition number of matrix A essentially says how good vector c can be restored from measurements y. Changing the order of rows clearly does not change the condition number. But is there information/literature on how to...

Homework Statement Three charges are in a straight row. The first charge has a value of 5.00 x 10-5 C. The second charge also has a value of 5.00 x 10-5 C and is 2.50 cm to the right of the first charge. The third charge has a value of -2.50 x 10-5 C and is 2.00 cm to the right of the...

I'm having trouble wrapping my head around what should be a trivial detail, but it is important, so hopefully someone else putting it in explicit words might help me understand it. What I am having trouble grasping is why do row operations preserve linear dependence relations for the columns...

Hi, Can anyone help me to inverse the below matrix by row reduction method. I know determinant method but I don't know row reduction method please help me. 4 5 -2 6 thanks.

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

I still want to be a physicist. I want to go back to school next fall, but haven't really made plans yet. I went to university for one year after high school, failed one semester and withdrew the next before being kicked out of the dorms for smoking pot. The next 3 years I attended a local...

I'm working with this excercise: make a program that gives the number of consecutive letters of a word and the most repeated letter in a row -example: if i enter aaafdseergftth and i press return the program should return a = 3, e=2, t=2 and a=3-. I've come up with a couple of "solutions"...

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...

Homework Statement I have to analyse the power output of a solar panel using a basic electrical engineering circuit analysis of a solar module if a complete row of solar cells in it is shadowed (For example, such shading might be caused by dust that slides down the surface of inclined panels.)...

Hi, My textbooks say that when a solution, x, is found to Ax=b it has a particular solution, x_0, such that A*x_0=b which is then combined with other solutions from the null space, n_i, such that A*n_i=0. However, when playing about with this I seem to have come across a problem. for...

1. Solve the matrix using elementary row operations 2. {3, 1, 4 1, 4, 3 4, 3, 1} 3. I keep trying to solve this, but I keep getting odd numbers, can someone help?

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...

I'm working on a project for myself that I started some time ago. This question only covers a small part of what I am doing. In my program I have vertices that I read in from a text file. They are read and stored in a matrix where each row of the matrix is a facet (triangle) created by the 2...

Homework Statement Find a formula for the sum of the elements of the nth row of Pascal's Triangle Homework Equations C(n,r) = [C(n-1,r-1) + C(n-1,r)] C(n,0) = C(n,n) = 1 The Attempt at a Solution I started with the summation of the elements in the rows n \sum^{n}_{r=0} C(n,r)...

Hello, Homework Statement Could anyone please explain why the row space of a matrix mXn over R is a subspace of R^n, and not of R^m? Homework Equations The Attempt at a Solution

Hi there, I've been having trouble with 2 algebra questions, I was hoping someone here could give me a hand. Homework Statement (i) Consider the function R2 → R2 defined by f (x, y) = (3x − 4y, x − 2y). Let v = (a, b) be the vector such that f (v) = (4, 6). Find the vector v and hence...

Prove that the rᵗʰ term in the nᵗʰ row of Pascal's triangle is nCr. nCr formula: n!/r!(n-r)! I've tried everything I can but I don't know how to approach this question.

Homework Statement http://puu.sh/1rcsO I got the first one from a simple scaling, but I can not figure out the second one. Homework Equations Det(cA) = cDet(A) Scaling a row scales the determinant Adding rows/columns to each other does not affect the determinant Det(AT) = Det A...

Hey, I'm having trouble understanding the trends of the oxidation states for the first row of the transition metals -my prof said that Cu is the only metal that forms a stable +1 oxidation state. But, I've done a question in hmwrk that had Cu+1 as unstable with respect to disproportionation how...

I am wondering about the relation betwen RRE forms and identity matrices. Consider the reduced row echelon form of any square matrix. Must this reduced row echelon form of the matrix necessarily be an identity matrix? I would suppose yes, but can this fact be proven? Could anyone provide an...

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...

Homework Statement You have 10 pieces of fruits of which 1 is an orange, 1 is an apple, 1 is a pear, and 1 is a peach. How many ways are there to organize them in a row if the apples and oranges must be together and the pears and peaches cannot be together. Homework Equations Mostly...

Need a lot of help here guys. I need to prove that for an nxn matrix A, if i interchange two rows to obtain B, then det=-detA I have proved my basis (below), but I'm stuck on the hard part, the induction (which I'm required to do). I understand the steps of induction, but i don't know how...

Why is row space of a matrix important?

Why is the row space of a matrix important?

Why do we solve for only the pivot variables when we are trying to solve a system of equations using reduced row echelon form? Thank you

I'm trying to find the determinant of a band diagonal matrix that has a parameter, κ, in some of the entries. Some entries are just numerical ones, others (κ X number), while others are (κ + number). I have been told that they way to solve for κ is to find the determinant of the this matrix and...

You can play against player A or player B in an all-skill game (such as chess or checkers). Suppose there are no ties/draws. On average you beat player A 90% of the time in this game, and on average you beat player B 10% in this game. You will play three games in row, and each game will be...

HI there. I'm taking Linear Algebra classes right now and this question has been bugging me. Homework Statement Find a general solution to the system, state the dimension of the solution space, and confirm the row vectors of A are orthogonal to the solution vectors. The given system is: (x1)...

if you perform row operations on a matrix A to convert it to the identity matrix and then use the same row operations and apply it to another matrix B, why is it that the end result of B^r does not depends on B's actual sequence

I want to create row matrix A by using row matrix B_1 , B_2 , B_3 ,...,B_7 Example B_1 = [1 2 3]; B_2 = [6 9 3]; B_3 = [4 7 5]; . . . B_7 = [9 6 3]; Then A = [1 2 3 6 9 3 4 7 5 ... 9 6 3]; My way is mea = input('Insert MEA No. :'); y = load(sprintf('%d.txt',mea),'-ascii'); for i=1:7...

That’s an old time question that it’s still a mistery to me. It’s a lot of time that I am trying to find an answer, but no text is clear on the topic and I am basically self-taught. What’s the difference between row vectors and column vectors? I came to this question when I found that the...

I asked this question on one another forum but didn't get any answer . Consider the following array of natural numbers : \begin{array}{ccccccccc} 1 & 2 & 4 & 7 & 11 & 16 & 22 & 29 & \ldots \\ 3 & 5 & 8 & 12 & 17 & 23 & 30 & 38 & \ldots \\ 6 & 9 & 13 & 18 & 24 & 31 & 39 & 48 & \ldots...

Ok, so I am taking my first course in linear algebra, and even though I am not a math major (physics major actually), I can't help but wish my teacher and text were more rigorous. So let me start by telling you all the problem I am having: (First question) My book states the following...

"Ax=b; every vector b is exactly from one vector x (from row space of A)".. <more>? Hi, I m referring 'Linear Algebra and its applications by Gilbert Starng". I read (ch.3.1)"Matrix transforms every vector from its row space to its column space". Or if given Ax=b; every vector b is...

Homework Statement Determine if vectors <1,-1,0,2,3> <1,0,-1,3,3> <1,-1,0,3,0> <0,1,-1,2,-2> are linearly dependent or independentHomework Equations I have been solving these questions in the book using a matrix and row reducing them. If I wound up with a free variable, I determined the...

I am trying to fully understand this theorem Theorem: Let A be an m x n matrix. The following are all true or all false. 1. For each b in Rm, the equation Ax has a solution 2. Each b in Rm is a linear combination of the columns of A. 3. The columns of A span Rm 4. A has a pivot position...

Homework Statement Determine the values of k for which the system of linear equations has (i) a unique solution, (ii) no solution, (iii) infinitely many solutions. Write down the complete solution in cases (i) and (iii): x + y + kz = 1 x + ky + z = 1 kx + y + z = 1 Homework Equations...

i know you have the 3 row operations. add two rows. multiply a row by a constant. add a multiple of a row to another. my question is can you multiply a row by a constant to clear a fraction at any time so long as you end up in row echelon form. no matter what operations you do the result in...

Hi- I am taking linear algebra and the teacher threw some problems at us that I cannot seem to figure out or find examples for online. Also, the textbook doesn't even cover the material. The problem states: Using Gauss-Jordan elimination, solve the following system with coefficients in...

Let's prove the uniqueness of row echelon form (Suppose we already knew existence) First, for any m*n matrix A, think about homogeneous equation AX=0. Obviously, AX=0 has a solution X=0, so its solution set is not empty. And A's row echelon form has same solution set. So if there are more...

Is the following statement correct? To find the rank of a matrix, reduce the matrix using elementary row operations to row-echelon form. Count the number of not-all-zero rows and not-all-zero columns. The rank is smaller of those 2 numbers.

Suppose you weren't allowed to switch rows, would it then always be possible to turn a regular matrix into the unit matrix or would the operation be needed in some cases?

EQUALITY OF ROW AND COLUMN RANK (o'Neil's proof) Is there smt wrong? http://www.mediafire.com/imageview.php?quickkey=znorkrmk3k1otjd&thumb=6 Theorem 7.9: EQUALITY OF ROW AND COLUMN RANK Proof: Page 210. It writes:... so the dimension of this column space is AT MOST r (equal to r if...

Homework Statement The 3x3 matrix A is transformed into I by the following elementary row operations R1+2R3 -> R1 R2+2R3 ->R2 2R2 ->R2 R1 <->R2 2R3 ->R3 Find det(A) Homework Equations I assumed to start off with the problem since I was going backwards from I to A. I would do the opposite of...

Homework Statement 28. Let A be an m x n matrix with a row consisting entirely of zeros. Show that if B is an n x p matrix, then BA has a row of zeros. Homework Equations N/AThe Attempt at a Solution A = (aij)_{mxn} and B = (bij)_{nxp}. Assuming that the entries for jth column of A are all...

Homework Statement How to verify that the nullspace is orthogonal to the row space of B? I have inserted the screen-shot of the problem below: http://i29.fastpic.ru/big/2011/0918/10/ca341692cc37b831143f5fe32351db10.jpg Homework Equations Nullspace and orthogonality.The Attempt at a Solution I...

Homework Statement Consider the following 3 row operations performed to a 4x3 matrix A used to transform it into matrix B: E1: -4R1+R4-> R4 E2: R2<->R3 E3: (1/2)R4-> R4 From there I am asked to find E1, E2, E3. The Attempt at a Solution I assumed the identity matrix I would start...

Linear Algebra Row Reduction? Homework Statement This question is frustrating me, and I might be missing the obvious, I tend to make algebraic mistakes, but I don't know what I'm doing wrong here! I'm trying to solve this system using row reduction: x-5y+4z=-3 2x-7y+3z=-2...

Homework Statement Consider three charges arranged as shown. + + - 1 2 3 What is the magnitude of the electric field strength at a point 1.5 cm to the left of the middle charge? The value of the Coulomb constant is 8.98755 × 10^9N
m2/C2. Answer in units of N/C q1=8.2 µC= 8.2*10^-6...