Row Definition and 220 Threads

[b]1. My question is a general question that I need the answer to so that I can fully understand the homework I am doing. When do I write given vectors as columns of a matrix, and when do I write them as rows of a matrix? More specifically, how do I write the vectors when finding: 1) Ker(T)...

Homework Statement Find the basis for the row space The Attempt at a Solution the given matrix is 0 1 2 1 2 1 0 2 0 2 1 1 So i reduced to row-echeleon form 2 1 0 2 0 1 2 1 0 0 3 1 so then rank = 3. My textbook states that the basis of the row space are the row vectors of leading ones...

I'm having a problem with this rule in general. Apparently one can calculate the determinant by multiplying the cofactors and entries of any row or any column of a matrix. I have a negative that pops up. I'll take a 3X3 matrix for simplicity. A= |a b c| |d e f| |g h i|...

My regards to all I am current doing my thesis for my masters. I have completed my work, but i seemed to have taken one thing for granted. lets assume there is a Single Row, Deep Groove Ball Bearing. Here what i want to know is CAN the outer ring and inner ring move at two different...

A , B are nXn matrices and AB=(A)^t t-is transpose prove that the space spanned by A's row equals the space spanned by A's columns i know that there dimentions are equals so in order to prove equality i need to prove that one is a part of the other how to do it? each column i of...

Are you allowed to mix and match row and column operations? For (a), using only row operations, I cannot get the matrix into the form they want. Could I swap a few of the columns around to do so? For (b), I got it into the form they want. The rank of the matrix is 2 because I have I2 there...

if i have a 4x3 matrix, this means there are more equations than unknowns and so there are no solutions to the system. does this mean that the row vectors are linearly dependent?

I'm having difficulty understanding the concepts presented in the following question. I'm given a matrix, [2,4,1,2,6; 1,2,1,0,1; ,-1,-2,-2,3,6; 1,2,-1,5,12], which is the matrix representation of a linear operator from R5 to R4. The question asks me to find a basis of the image and the...

show that if all the row sums of a matrix A belong to C (nxm) are zeroes, then A is singular. Hint. Observe that Ax=0 for x=[1 1 ...1]T

which are the the simpliest properties of a (0,1)-matrix with constant row sum 3 *this matrix is a matrix D which dirives from a linear system of the form Ci=Xi+Xai+Xbi ai,bi Ε {1,2,..,k} , i=1,2,...,k or C=DX in the formal language of matrices, thus...

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.

Homework Statement I need to argue this properly Let's say I have a matrix A and rref(A) is given as \begin{bmatrix} 1 & 0&-1 \\ 0& 1 & -1 \end{bmatrix} Since I have a pivot in every row, why isn't this linearly independent? Don't give me other arguments like "because there...

Homework Statement This is just a conceptual question Whenever you are asked for a basis for the subspace spanner by some set of vectors, is that the same as asking the basis that forms the column space of that matrix? Are the dimension for that subspace the same as the column space...

This isn't homework. I asked my professor for help on figuring out a way to know the possible combinations of reduced row echelon forms of nxn matrices, or mxn matrices. He only could show me why it was really hard to find this out, not how to actually do it. His method was to use...

Hi Again: Just curious: I know that, given a system of linear equations, ERO's (scaling both sides of an equation, exchanging/swapping rows and adding a multiple of a row to another row) preserve solutions, i.e., if x is a solution to Ax=b, then swapping rows will preserve x as a...

Hi, Everyone: A question about finding the inverse of a matrix M using elementary row operations (ERO's) E_k (where E_k is either a row-exchange, a scaling of a row by k, or adding the multiple of one row to another row ) to do row-reduction in reduced-row-echelon format, to end...

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...

Homework Statement I am having trouble row reducing... 5cos(t) 5sin(t) | -cos(t) 2cos(t)+sin(t) 2sin(t)-cos(t) | sin(t) Homework Equations The Attempt at a Solution I know I am allowed to multiply a row by a constant but I...

How exactly do you decide which operations to do in doing a matrix row reduction? Every example I see just randomly multiplies the rows or does row operations and magically they get the answer. HOW do you know to do certain operations? I understand the reduced row echelon form but it still...

I would like to take a row vector of my choosing and see if it matches any other rows in say a 1e6 x 100 array. I want to do this as fast as possible with matlab. There should only be, if any, one match with the actual data I'll be using because every row in my data (the matrix) will be...

After the eigendecomposition of the following matrix is performed, I wonder what happens to the eigenvectors and eigenvalues of the matrix obtained by flipping rows of the original. Say the original is 0 5 7 8 5 0 2 9 7 2 0 3 8 9 3 0 and the flipped version is: 5 0 2 9 8 9 3 0 7 2 0 3 0...

A row contains 1000 integers The second row is formed by writing under each integer, the number of times it occurs in the first row.The third row is now constructed by writing under each number in the 2nd row, the number of times it occurs in the 2nd row.This is process is continued Prove...

Hi..I have a very basic query...while solving a determinant, when we exchange/swap 2 rows we need to add a negative sign to the determinant. However, when we are trying to reduce a matrix to a row echelon form, when we swap 2 rows..do we need to add a negatice sign here as well? Well..from what...

Homework Statement I need to find the x,y coordinates of the points that neighbor a center point that has been rotated around yet another point. An illustration is best: http://coldconstructs.com/random/point_prob.png Given: point of origin, angle, p1, p2 Needed: p1 a, b, c etc, p2 a, b, c...

Dispersion Relation: w2=B(1/m+1/M)+-SQRT[(1/m+1/M)2-(4sin2ka/mM)] For waves on a diatomic row of masses, what is the physical meaning of acoustic and optical branches of this dispersion relation? What is the expression for the maximum frequency of the optical branch? Really stuck on...

A = 1 2 -1 3 3 5 2 0 0 1 2 1 -1 0 -2 7 Problem: Find a basis for the row space of A consisting of vectors that are row vector of A. My attempt: I transpose the matrix A and put it into reduced row echelon form. It turns out that there are leading ones in every column...

Hello all, I have been studying some linear algebra, and I recently came upon the method of finding determinants by row reduction (to row echelon form). But isn't it true than a matrix can have any row echelon form? If so, this would mean different determinants, right? I am studying from...

Is row echelon form an upper triangular matrix? if so, does this mean that its determinant could be 1 or 0? Even if its row equivalent has a different determinant? Please Answer and thanks.

The subspace formed by matrix A and A' will be same or different if A' is obtained by applying an elementary row operation on A? Please prove it.

So I just started my Linear Algebra course yesterday. I am confused on one aspect. When asked to solve an augmented matrix, the teacher would employ row operations. I understand how the row operations lead from one matrix to the next, but what I don't understand is how we formulate which row...

Say I am given a matrix and am supposed to put the matrix in row echelon form, does swapping two rows change the final matrix? Say I have: 3 1 4 1 1 1 0 1 3 It would save time to swap the first two rows, however when I do that on my problems the first row is wrong.

My book gives the following definition for reduced row echelon form: 1) If a row has nonzero entries, then the first nonzero entry is 1, called the leading 1 in this row. 2) If a column contains a leading 1, then all other entries in that column are zero. 3) If a row contains a leading 1...

Every matrix is row equivalent to a unique matrix in echelon form? False, a matrix is row equivalent if it is non-singular. Is the above correct reasoning for the initial statement.

Homework Statement Well, let's take F: x^2 y^3=0 . Now, let's say thay y=y(x), y being an implicit function of x. I want to find 2nd row derivative \frac{d^2y}{dx^2} using differential operator. Homework Equations not apply The Attempt at a Solution Using D for the first...

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...

Homework Statement If A is an m x n matrix, show that null(A) = [row(A)]_|_ (meaning rowA perp). I handed in an assignment with this question on it, and got zero points. I think what I did is mostly right, but I want someone to make sure I'm not out to lunch before I go to my prof...

Homework Statement [PLAIN]http://img260.imageshack.us/img260/727/picture2mg.png just wondering.. isn't the the matrix on the 1st line already in its reduced row echelon form? why is another row operation required to obtain the matrix on the 2nd line? (notice the changes to the matrix on the...

Hello All, I am trying to learn matrix compression algorithms for sparse matrices. I understand the Compressed Row Storage (CRS) format but I am having difficulty with the Block Compressed Row Storage (BCRS) format - where the size of the sub-block(s) are 2x2. Can anyone please point me to...

If n*n matrix, can row space ever be equal to null space? P.S.: this is NOT a homework question. It's a general question to get the concepts straight in my head.

Homework Statement http://img708.imageshack.us/img708/7309/10324398.jpg The Attempt at a Solution First I row reduced the matrix into the RREF and got \left[ \begin{array}{cccc} 1 & 0 & -1 & -2 \\ 0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 0 \end{array} \right] (0,1,2,3) is a linear...

Homework Statement Say you had an augmented matrix 0 1 0 0 0 0 1 0 0 0 0 0 You would get... x2=0 x3=0 x1= arbitrary? What exactly is meant by arbitrary? Does this mean that x1 could be anything? and if so does that mean that the system has an infinite amount of...

Hello everyone, When you go on a boat and use the paddle and displace water molecules you create low water pressure right? Then why does the boat move forward? I know water would flow from high to low but how can you specfically know that water would fly from high to low in forward direction...

A particular introduction to matrices involved viewing them as an array/list of vectors (column vectors) in Rn. The problem I see in this is that it is sort of like saying that a row of a matrix is a vector along the same degree of freedom (elements of the same row are elements of different...

The question reads "Use the reduced row echelon forms that you computed to describe the solution set for each of two linear systems we consider". What I don't understand is what it means by The solution set for each of the two linear systems. Could someone clear this up for me. Any help...

What exactly is a reduced row echelon matrix. I had to convert this to one: 1 2 1 1 1 1 -3 -6 -2 0 -1 -3 2 4 2 1 3 -3 And got: 1 2 1 1 1 1 0 0 1 3 2 0 0 0 0 1 -1 5 Is this right and, if not, why? Thanks for the...

Homework Statement Show that a matrix with a row of zeros cannot have an inverse. The Attempt at a Solution I believe that I have to use the definition of invertible to do this. If A is an nxn matrix and there exists some matrix B such that AB = BA = I where I is the identity. I...

Homework Statement Give a least squares solution to Ax=C and give the residual error A= -1, 1, 2; 1, -1, 0; 1, -1, 2; C= -1; -1; 2; Homework Equations Residual Error= |Ax-C| The Attempt at a Solution I have done an RREF on the Transpose of A times A...

Homework Statement Show that any multiple of a row can be added to a row above it by row operations of other types. Homework Equations There are only 3 elementary row operations. i. Interchange two rows ii. Multiply a row by a constant iii. Add a multiple of a row to another row. The...

For the two matrices A and B, (AB)i,j = ri . dj ---- . 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 the column vectors...

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...