Echelon Definition and 49 Threads

Hey! :giggle: Let \begin{equation*}A=\begin{pmatrix}0 & -2 & 2 & 0 & 0 & -6 \\ 0 & 0 & 0 & 1 & 1 & 3\\ 0 & 0 & 0 & 1 & -1 & -1 \\ 0 & 1 & -1 & 0 & 2 & 7\\ 0 & 3 & -3 & 1 & 2 & 14\end{pmatrix}, \ b_1=\begin{pmatrix}0 \\ 0 \\ 0 \\ 0 \\ 0\end{pmatrix} , \ b_2=\begin{pmatrix}-2 \\ 1 \\ -1 \\ 3 \\...

The first thing I do is making the argumented matrix: Then I try to rearrange to make the row echelon form. But maybe that's what confusses me the most. I have tried different ways of doing it, for example changing the order of the equations. I always end up with ##k+number## expression in...

Hey! 😊 I am looking at the following exercise but I think that I miss something. The statement is the following: We are given the following system of equations: \begin{align*}2a-2c+d-2e=&-2 \\ -2c-2d+2e=&\ \ \ \ \ 3 \\ d+2e=&-2\end{align*} 1) Is the system in echelon form? Justify. 2)...

Hey! :o Let $\displaystyle{a:=\begin{pmatrix}2 & 1 & 0 & 5 \\ 1 & 0 & 1 & 1 \\ 4 & 1 &2 & 7\end{pmatrix}\in \mathbb{R}^{3\times4}}$ and $\displaystyle{b_1:=\begin{pmatrix}1 \\ 1 \\ 1\end{pmatrix} , \ b_2:=\begin{pmatrix}-2 \\ 1 \\ 0\end{pmatrix} \in \mathbb{R}^3}$. I applied the Gauss...

I'm doing problems on finding row and column spaces. My textbook tells me to find the echelon form of the matrix, and then to identify the bases. My question is, can I reduce the matrix to reduced echelon form to get the bases? I have the same question about bases for the solution space.

Hey! :o Let $$A=\begin{pmatrix}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{pmatrix}\in \mathbb{R}^{3\times 3}$$ I want to determine a matrix $C\in GL_3(\mathbb{R})$ such that $T:=C\cdot A$ has echelon form. Performing an elementary row operation is equivalent to multiplying an invertible matrix...

I need to find the echelon form of: 1 1 2 8 -1 -2 3 1 3 -7 4 10 and so far I have: 1 1 2 8 0 10 -50 -90 0 0 -52 -104 I was just wondering if I was required to put another zero in my third row. Am I always required to have three zeros in the third row? I'm assuming I do, but when I looked at...

$\textsf{a. Find the determinants by row reduction in echelon form.}$ $$\left| \begin{array}{rrr} 1&5&-6\\ -1&-4&4 \\ -2&-7 & 9 \end{array} \right|$$ ok i multiplied $r_1$ by 1 and added it to $r_2$ to get $$\left| \begin{array}{rrr} 1&5&-6\\ 0&1&-2 \\ -2&-7 & 9 \end{array} \right|$$...

Homework Statement (i) Reduce the system to echelon form C|d (ii) For k = -12, what are the ranks of C and C|d? Find the solution in vector form if the system is consistent. (iii) Repeat part (b) above for k = −18 Homework Equations Gaussian elimination I used here...

I understand that the RREF algorithm can be used on matrices representing systems of equations to find the solution set of that system. However, can this algorithm be used for any matrix of any size? For example, what if we, what if we had a 1x1 mattix, or a 2x1? What is the minimum size of a...

Homework Statement The assignment is to find all values of k (in R) for which the system has 0 solutions, 1 solution and infinite solutions. If there are infinite solutions, find the amount of free variables. The system of linear equations: kx + (k+1)y + z = 0 kx + y + (k+1)z = 0 2kx + y + z =...

Homework Statement Find the general solution Homework Equations Row operations Gaussian elimination The Attempt at a Solution This is has happened twice now and I'm not too sure how to deal with it. The last row ends up being all zeros except in that spot. I need to make this into an...

Hi everyone, I am teaching myself Linear Algebra and I am confused with the terminology used in the subject. I am studying Linear Algebra based on Anton's. In the textbook, an augmented matrix in REF needs to have the first nonzero number in a given row to be 1. However, in other textbooks...

This is actually a pretty simple thing, but the ref(A) that I compute on paper is different from the ref(A) that my TI-89 gives me. Compute ref(A) where A = \begin{bmatrix} 1 & 2\\ 3 & 8 \end{bmatrix} \\ \begin{bmatrix}1 & 2\\ 3 & 8\end{bmatrix} \ r_2 \rightarrow r_2 - 3 \times r_1 \\ \\...

I have x1 + 3x2 - x3 = b1 x1 - x2 + 3x3 = b1 -2x1 - 5x2 - x3 = b1 So using an augmented matrix I get this [1 3 -1 | 1] [1 -1 3 | 1] [-2 -5 1 | 1] [1 3 -1 | 1] [0 -4 4 | 0] R2 - R1 = R2 [0 1 -1 | 3] R3 + 2R1 = R3 [1 3 -1 | 1] [0 1 -1 | 3] Swap R2 with R3 [0 -4 4 | 0] [1 0 2 | -8] R1 - 3R2 =...

Homework Statement Problem: Consider a system of linear equations in echelon form with r equations and n unknowns. Prove the following.: (i) If r = n, then the system has a unique solution. (ii) If r < n, then we can arbitrarily assign values to the n - r free variables and solve uniquely...

For some reason I just can't seem to wrap my head around the idea of reducing a Matrix to row echelon form. I'm familiar with the steps that the textbooks and tutorials use and how it's done but when I try practicing on my own I feel lost. e.g. all I end up with are just a bunch of random...

Homework Statement Is the reduced echelon form of a matrix unique? Justify your conclusion. Namely, suppose that by performing some row operations (not necessarily following any algorithm) we end up with a reduced echelon matrix. Do we always end up with the same matrix, or can we get different...

Please check my solution.View image: Possible Echelon Form of Matrix

Please Check My Solution View image: Possible Echelon Form of Matrix

Homework Statement In each part, the reduced echelon form of the augmented matrix of a system of linear equations is given. Find all solutions to the original system. a.  [1 0] [2] [0 1] [5]  b.  [1 0] [2] [0 0] [1]  c.  [1 0] [2] [0 0] [0]  d. ...

I'm doing my homework but I'm lost on one thing. Let's say that we have a systems of equations like so: 2x1+3x2=y1 4x1+2x2=y2 Instead of setting it to a constant our teacher sets it to a variable, he says that to be able to compute this, the augmented matrix should look like: 2 3|1 0 4 1|0 1...

Hello, I have the following system of linear equations - kx + 3y -z = 1 x + 2y - z = 2 -kx + y + 2z = -1 I have reduced it to 1 2 -1 : 2 0 1 1/4 : 0 0 0 (7-6k)/7k : (8-4k)/7 assuming k ≠ 0. I would now like to be able to determine...

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...

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

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...

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?

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...

Homework Statement What is the reduced echelon form of a n x n nonsingular matrix? Briefly explain.Homework Equations The Attempt at a Solution I know that a n x n nonsingular matrix will always result in echelon form will always have a diagonal orientation with a single digit in its own row...

Homework Statement If my original echelon form is: 1 1 -2 1 | 2 0 3 3 3 | -3 0 0 0 1 | -4 and according to my notes that my teacher provided, the reduced form is: 1 0 -3 0 | 3 0 1 1 0 | 3 0 0 0 1 | -4 he noted that in the reduced form, the 1's in columns 1, 2, and 4 are...

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...

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...

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.

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...

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...

Homework Statement Suppose I have the augmented matrix 0 -1 0 | 0 0 -6 3 | 0 0 -1 0 | 0 Homework Equations which equates to -y = 0 and -6y + 3z = 0. The Attempt at a Solution Would the solution be that x, y and z all equal 0? Or do I need to let...

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 Give all the possible 2x2 row echelon reduced matrices. 2. The attempt at a solution I thought about the matrices (0 0, 0 0), (1 0, 0 0), (0 1, 0 0), (0 0, 1 0), (1 0, 0 1), (0 1, 0 0), (0 0, 0 1). Where the "," inside the parenthesis means a change of row. So in...

Homework Statement Let T: R4 --> R4 be defined by T(a,b,c,d) = (4a-b+c, b+3d, 3a+c+d, c-d, b+c+2d) where a,b,c,d are in R. Compute rank(T). Homework Equations The Attempt at a Solution Writing the transformation as a matrix, T[a] = [4 -1 1 0][a] [b] [0 1 0...

So google has yielded no good results. When I "transform" a matrix to row echelon form, not reduced row echelon form (leading entries are not necessarily 1), what does it mean if my last row is all 0's? Another thing, when setting up the equations as a matrix, do I include the solutions of the...

I am having problems with understanding the whole concept/how to compute the row-reduced echelon form. Can someone please help me? Thanks

Homework Statement i'm trying to put the 3x3 matrix: [4 2 6] [ 2 8 2] [-1 3 1] into row echelow from. but i don't know where I'm goin wrong in my row operations. could some1 please tell me where i hav...

Problem statement: Find the determinant of the following matrix by row reduction to echelon form. |1 3 3 -4 | |0 1 2 -5 | |2 5 4 -3 | |-3 -7 -5 2 | I reduced this matrix to |1 3 3 -4 | |0 1 2 -5 | |0 -1 -2 5 | |0 2 4...

Here's the problem: given in echelon form, the column space basis is [5,0,0,0]^t, [4,2,0,0]^t and the question is to find another matrix A with the same echelon form but different basis... how do i find a different basis? thanks

How do you know, when you have to stop row-equivalent operations when you are trying to get a 'reduced row-echelon' form of a given matrix. Is it necessary to have all the columns with pivot element as 1 and rest as 0? do you need to continue the operation if you already have a all 0 row? I want...

Hello everyone The reduced row-echelon forms of the augmented matrices of four systems are given below. How many solutions does each system have? Here is the matrices: 1 0 -12 0 0 1 0 0 0 0 0 1 0 0 0 0 A. Infinitely many solutions B. No solutions C. Unique solution D. None of the...

i have a matrix in reduced row echelon form and it gives me the equations x1+x2=-27.5, x3=-13.5, and x4 = 15. how do i solve for x1 and x2