Row Definition and 212 Threads

The title pretty much says it... I know that in general eigenvalues are not necessarily preserved when matrix rows or columns are swapped. But in many cases it seems they are, at least with 4x4 matrices. So is there some specific rule that says when eigenvalues are preserved if I swap two rows...

I have tried row reduction to solve for the first eigenvector but I don't feel like I get any closer to the solution:

Hi! Please, could you help me on how to solve the following matrix ? I need to replace the value 3 on the third line by 0, the first column need to remain zero and 1 for the third column. I'm having a lot of difficulties with this. How would you proceed ? Thank you for your time and help...

How do I calculate a 3x3 matrix multiplication with a 3 column row vector, like below? ## \begin{bmatrix} A11 & A12 & A13\\ A21 & A22 & A23\\ A31 & A32 & A33 \end{bmatrix}\begin{bmatrix} B1 & B2 & B3 \end{bmatrix} ##

Dear Everybody, I have some trouble with this problem: Finding a sequence of elementary matrix for this matrix A. Let ##A=\begin{bmatrix} 4 & -1 \\ 3& -1\end{bmatrix}##. I first used the ##\frac{1}{4}R1##-> ##R1##. So the ##E_1=\begin{bmatrix} \frac{1}{4} & 0 \\ 0& 1\end{bmatrix}##. So the...

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 \\...

$\tiny{307.1.1}$ Use row reduction on the appropriate augmented matrix to solve the following system of equations: $\begin{array}{ll}3x+2y&=2\\x-y&=1\end{array} \sim\left[\begin{array}{rr|r}3&2&2\\ \:1&-1&1\end{array}\right]\sim \begin{bmatrix}1&0&\frac{4}{5}\\ 0&1&-\frac{1}{5}\end{bmatrix}$...

$\left[ \begin{array}{rrrr|r} 1& -5& 4& 0&0\\ 0& 1& 0& 1&0\\ 0& 0& 3& 0&0\\ 0& 0& 0& 2&0 \end{array}\right] $ OK my first move on this is $r_3/3$ and $r_4/2$. $\left[ \begin{array}{rrrr|r} 1& -5& 4& 0&0\\ 0& 1& 0& 1&0\\ 0& 0& 1& 0&0\\ 0& 0& 0& 1&0 \end{array}\right]$ $r_2-r_4=r_2\quad$ doesn't...

Hey! :o We have the matrices \begin{equation*}a=\begin{pmatrix}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{pmatrix}, \ \ E_{1,3}=\begin{pmatrix}0 & 0 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{pmatrix}, \ \ u_n=\begin{pmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 &0 & 1\end{pmatrix}\end{equation*} I have...

Show that a square matrix with a zero row is not invertible. first a matrix has to be a square to be invertable if $$\det \begin{pmatrix}1&0&0\\ 0&1&0\\ 3&0&1\end{pmatrix}=1$$ then $$\begin{pmatrix} 1&0&0\\ 0&1&0\\ 3&0&1\end{pmatrix}^{-1} =\begin{pmatrix}1&0&0\\ 0&1&0\\ -3&0&1...

I realize this is probably quite easy and basic but I just can't get comfortable with calculators to work it our with any certainty. There are 100 socks in a drawer. 84 are Red. 16 are White. If you are blindfolded & have to choose 11 socks randomly, what is the odds or what it more likely...

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.

Homework Statement We have a coin with probability ##0\leqslant p \leqslant 1## of getting heads. We flip the coin until we get ##7## heads in a row. Let ##N_7## be the number of necessary flips to get the ##7## heads in a row. What is the expected value ##E(N_7)##? Homework Equations The...

i have a dataset that has the timestamp data within each row and I am trying to plot the values to see the distribution but have no idea how to do it if the data is presented this way as attached. any ideas? thanks

Hello, I'm looking for a way to create an approximate row-orthonormal matrix with the number of rows (m) > the number of columns (n); i.e., finding A(mxn) so that A(mxn) . A^T(nxm) = I(mxm). I used singular value decomposition (e.g., DGESVD in mkl mathlib), but what I actually got was an...

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

Hi, I hope someone can help. I'm wanting to get a better grasp on the connection between the row picture v.s. the column picture of linear systems and their solutions. In the picture below, the row picture are the three graphs on the top and their corresponding column pictures are below them...

Prove that interchange of two rows of a matrix can be accomplished by a finite sequence of elemenatary row operations of the other two types. My proof :- If ##A_k## is to be interchanged by ##A_l## then, ##\displaystyle \begin{align} A_k &\to A_l + A_k \\ A_l &\to - A_l \\ A_l &\to A_k + A_l...

Hello there. I'm currently trying to come to terms with the aforementioned topics. As I am self studying, a full understanding of these concepts escapes me. There's something I'm not grasping here and I would like to discuss these to clear away the clouds. As I understand it, a basis for some...

The question below could also be re-phrased in terms of functions of one variable (using indexes). However, it seems it is easier to explain it with two variables. Here is the question: Suppose we have some total recursive function f: N x N→N. Define the n-th row of f as the function Fn : N→N...

Homework Statement Show that elementary row operations don't affect solutions sets in linear systems Homework Equations - The Attempt at a Solution It's pretty easy to come up with a random linear system and perform ERO on them and showing that solutions are not affected, but is there all...

Here are some first row BDE's (in kcal/mol): H-CH3 = 105 <---> [H]+ [CH3]- H-NH2 = 103 H-OH = 119 H-F = 136 <---> [H]+ [F]- This trend is often rationalized in terms of increasing ionic character (or with no-bond resonance). However, the H-NH2 BDE should have a higher ionic contribution than...

Homework Statement We're given some linear transformations, and asked what the null space, column space and row space of the matrix representations tell us Homework EquationsThe Attempt at a Solution I know what information the column space and null space contain, but what does the row space of...

Suppose that I have an overdetermined equation system in matrix form: Ax = b Where x and b are column vectors, and A has the same number of rows as b, and x has less rows than both. The least-squares method could be used here to obtain the best possible approximative solution. Let's call this...

Homework Statement Show that the determinant of is (a-b)(b-c)(c-a) Homework Equations Row reduction, determinants The Attempt at a Solution Apparently I got a (a-b)^2 instead of (a-b) when I multiplied them up. It would be grateful if someone can point me out where the mistakes are.

Suppose, ##A## is an idempotent matrix, i.e, ##A^2=A##. For idempotent matrix, the eigenvalues are ##1## and ##0##. Here, the eigenspace corresponding to eigenvalue ##1## is the column space, and the eigenspace corresponding to eigenvalue ##0## is the null space. But eigenspaces for distinct...

the answer key said d is supposed to be 10. but there's a way to evade that row exchange. 1st picture is the question and the 2nd picture is the elimination steps.

Homework Statement [/B] In a tower a princess throws a ladder of 20 plates of thickness d and mass m each, which are connected with springs of constant k and loose length l0. the window is at height H. 1) What's the elongation of each of the spring pairs? 2) What's the total ladder's length. 3)...

Homework Statement Multiply these row excahnge matrices in the order pq qp and p^2 p = [0 1 0] [1 0 0] [0 0 1] q= [0 0 1] [0 1 0] [1 0 0] Homework EquationsThe Attempt at a Solution I don't understand why the solution is [0 1 0] [0 0 1] [1 0 0] do you not multiply rows by columns? When i...

I am having trouble with the following problem; a.) Find a matrix B in reduced echelon form such that B is row equivalent to the given matrix A. A=$$\left[\begin{array}{c}1 & 2 & 3 & -1 \\ 3 & 5 & 8 & -2 \\ 1 & 1 & 2 & 0 \end{array}\right]$$ So using my calculator I am able to get...

I've managed to distill the rambling into just this question, posted here and at the end of my digressive thoughts as well: "Will we always be able to split x up in such a way that we have a nullspace component and a non-row space component?" Take a matrix A = \begin{bmatrix}1 & 2\\ 3 &...

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 \\ \\...

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...

I'm not sure if corrosion does have a significant effect on copper in general but if it does, how and why does it happen, and the process of it happening and its effect on the overall resistivity? This is for a physics assignment...Please help if you can. Thank you

Homework Statement Show that the given matrices are row equivalent and find a sequence of elementary row ops that will convert A into B. a = 2 0 -1 1 1 0 -1 1 1 b = 3 1 -1 3 5 1 2 2 0 Homework EquationsThe...

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...

If you have two arbitrary matrices, A and B, I was wondering if row operations can be performed in any order to produce the same results. For example, you perform elementary row operations on A to produce A', then do A' - B, then also produce a new matrix through elementary row operations on...

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...

With 6 red, 3 blue and 3 green flower pots, how many color permutations in row of 12 are there ? Its not 12! or n!/(n-r)!

What would the probability be of 10 randomly generated numbers producing exactly 3 0s in a row at any point in the 10 entries? Ex: 1. 5 2. 0 3. 0 4. 0 5. 9 6. 8 7. 1 8. 0 9. 8 10. 2 Using a binomial distribution to find the probability of any 3 out of 10 I got: 1/10 chance of...

Homework Statement I am in a calculus class where we are learning the introduction to row reduction. I have done this before in other courses, so I am familiar with the process, but I am not sure about this one. We were given: x4 + 2x5- x6 = 2 x1 + 2x2 + x5 -x6 = 0 x1 + 2x2 + 2x3 - x5 +...

Homework Statement The number of ways in which 4 persons P1,P2,P3,P4 can be arranged in a row such that P2 does not follow P1, P3 does not follow P2 and P4 does not follow P3 is The Attempt at a Solution Let us assume that P1 occupies the first position. So, the next position can be...

hi guys as per title Yesterday, 10 March 2014 there was a M 6.8 offshore of northern California in the Mendocino Fracture Zone of the Juan De Fuca Plate Just coming in on the seismo right now is another M 6.8, east of the South Sandwich Islands right at the southern end of the Atlantic Ocean...

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 Write and row reduce the augmented matrix to find out whether the given set of equations has exactly one solution, no solutions, or infinitely many solutions. -x+y-z=4 x-y+2z=3 2x-2y+4z=6 Homework Equations The Attempt at a Solution I saw right away that...

Is it correct to say it doesn't matter if a row of zeros is added on to a matrix? For example does $$ \begin{bmatrix}1&2\\3&4 \end{bmatrix} = \begin{bmatrix}1&2\\3&4 \\ 0&0 \end{bmatrix}$$ Does it depend on context? For example if the matrix is representing a linear system of equations then...

If your betting on a coin flip but person a is the banker and person b can quit at any time, does person b have an advantage. The martingale theory of doubling a losing bet doesn't work if there is a maximum bet. Start at 5 and going to the max of 1000 a person can bet...

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...