Row Definition and 212 Threads

Homework Statement find the determinant using row operations: 1 -2 2 0 5 -1 2 -4 1 Homework Equations The Attempt at a Solution i took row 3 and took 2 x row 1 away from it to get : 1 -2 2 0 5 -1 0 0 -3 1 x 5 x (-3) = -15...but i multiplied a row by 2 so i should get -30...

Homework Statement I have a question about an old exam and i have no idea where to start. The question says: Find the vector in the row space A=[1 0 1 1 /new row 0 1 -1 1] 2x4 matrix nearest to the vector (1,1,-1,1) I have absolutely no clue how to start. Homework Equations The...

Why is it that a 16 comes out when you factor a 2 from each row of this matrix: 0 2 2 2 2 0 2 2 2 2 0 2 2 2 2 0

Homework Statement When row reducing and trying to find the pivots, does it matter if there is a zero on top? i.e.: 1 2 3 4 0 8 0 5 0 0 4 6 i know that the 1st and 2nd columns are pivots but is the 3rd column a pivot also?

which one of w1 or w2 linear independent of the v groupr?? i got to the situation that each one of them could be independant and the other not ?? the answer in the book is that w2 is independent and the other is not v_1=\begin{bmatrix} 1\\ 1\\ -2\\ 1 \end{bmatrix}...

Homework Statement In the following exercises verify that the row rank is equal to the column rank by explicitly finding the dimensions of the row space and the column space of the given matrix. A = [1 2 1 ; 2 1 -1] Homework Equations The Attempt at a Solution All i can...

Homework Statement A = [ 1 0 1 -1 1 -3 2 1 0] what is the column space of A? What is the row space of A What is the solution space of A? Also, if i were given a multiple choice, how do I check if a vector is in either the column, row or solution space of A ...

Homework Statement Demonstrate that a matrix that has a null row is not invertible. 2. The attempt at a solution I know that saying that a matrix A is invertible is equivalent to say that A is row-equivalent and column-equivalent to the identity matrix. And also that there exist elemental...

I was reading that the "exchange rows" operation can be achieved through the other two operations: multiplication by a nonzero number and adding a multiple of one row to another. Any thoughts on the actual algorithm for achieving an exchange of rows through these other two operations? I...

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...

http://news.yahoo.com/s/ap/20090110/ap_on_re_us/death_row_eye I can't believe they're going to execute him at all. If this isn't proof enough that he's insane, what would be? Here's his offender info: http://www.tdcj.state.tx.us/stat/thomasandre.htm

Homework Statement Can anyone help me figure out basis for RS(A) and basis for CS (A) along with their dimension? I mean dim CS(A) and dim RS(A) where A is [1 -2 4 1] [0 7 -15 -4] [0 0 0 0] Homework Equations The Attempt at a Solution are all non zero rows the basis for...

Homework Statement What are the basis for the row space and null space for the following matrix? Find the dimension of RS, dim of NS. [1 -2 4 1] [3 1 -3 -1] [5 -3 5 1] Homework Equations dim RS + dim NS = # of columns The Attempt at a Solution I reduced the matrix into...

Hello, I just started learning Elementary Linear Algebra. I've read through the first chapter in my book (Elementary Linear Algebra by Larson, Edwards, Falvo, 5th edition). There were two "Discovery" questions that try to see if you know how systems of equations work. I am unsure on both...

Understading row and column space Homework Statement I am having hard time trying to understand row and column space. Can anyone simplify the meanings of them so that i can visualize them well. Homework Equations dimension of row space = rank ? How? Why? The Attempt at a Solution...

Homework Statement a house plan has 3 different floor plans: Plan A- 3 three-bedroom units, 7 two-bedroom units, and 8 one-bedroom units Plan B- 4 three- bedroom units, 4 two-bedroom units, and 8 one-bedroom units Plan C- 5 three-bedroom units, 3 two-bedroom units, and 9 one bedroom units...

Homework Statement Find the condition of k such that the set of equations x+y-z=1, x+2y+kz=-1, x+ky-z=1, has a unique soltuion,infinite sol'n or no solution. Homework Equations The Attempt at a Solution In the augemented matrix form [1 1 -1 1] [1 2 k -1] [1 k -1 -1]...

A certain hallway contains a row of lockers numbered from 1 to 30. All the lockers are initially closed. 30 students are lined up in the hallway. The first student walks down the row and opens up all the lockers. The second student closes all the lockers numbered 2, 4, 6, ..., 30. The third...

Homework Statement Two lenses, one converging with focal length 20.0cm and one diverging with focal length -10.0cm, are placed 25.cm apart. An object is placed 60.0cm in front of the converging lense. Determine the position of the final image. Homework Equations \frac{1}{s_i} +...

[SOLVED] Proving col rank = row rank Homework Statement Demonstrate these four assertions to get an alternate proof that column rank equals row rank. (a) \vec{y}\cdot\vec{y} = \vec{0} \Leftrightarrow \vec{y} = \vec{0} (b) A\vec{x} = \vec{0} \Leftrightarrow A^TA\vec{x} = \vec{0} (c) \dim...

Hi, everybody. Could some one please help find the greatest number in each row of a matrix, this is what i have so far.. am i one the right track? (using C code) Float big; Big = -9999999.99999 for( i==0) { for( j = 0; j < n; j++) { if( *(mat + (j*0) + 0) > big) { bigc1 =...

Edit: My friend just explained it to me, duh! If the row adds to zero then (row)dot(1,1,...,1) = 0! And it is in the nullspace. Thanks anyway! :) Hi all. I've been learning about determinants and I was reading one of the sample problems in my textbook. I thought I understood the chapter...

Homework Statement In how many ways can eight identical rooks be placed on an ordinary 8x8 chessboard so that no two are in the same row or column? In how many ways, if each rook has a different color? Homework Equations I looked at the equation n choose k (nck), but I don't know if...

Hi All, I need to multiply column and row vectors but not sure that I am doing this right (on the picture below): http://img244.imageshack.us/img244/6222/35459606ye4.th.jpg Could you check it and correct if necessary? Thank you.

Hi, everyone: I was wondering about the relation of a matrix , seen as a linear map, and its row-reduced form, seen the same way. More specifically: take a matrix M , seen as a linear map L. What is the relation between this map L given by M, and the linear map L' given by...

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 just interested is there anyway to solve these through a specific method by hand. I know that you can produce an algorithm so that you can solve these into upper triangle form but is there a way to do it by hand other than by inspection.

Increasing Row Size... Homework Statement There are 150 rows at a concert hall. Each row you move back there is an increase of 10% in the number of seats. The first row has 100 seats. How many seats are there in the concert hall?Homework Equations I don't know the equation to represent this...

Hi, how would you go about calculating the probability that on any given day (24 hours) you toss heads say 20 times in a row. That is, let's say you continuously throw a coin, one toss per second. What's the probability that on a specific day there was one run of 20 heads in a row? I'm...

When I compile the following latex code on my computer, the subscript of the first row and the superscript of the second row overlap. Is there any way to make the rows farther apart? \begin{array}{ccccc} \cos^2\phi_y^1 - \cos^2\phi_x^1 & \cos^2\phi^1_z - \cos^2\phi_x^1 & 2\cos\phi_x^1...

What row of numbers comes next? 2 12 1112 3112 132112 1113122112 311311222112

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...

Homework Statement Find the inverse of by reducing the augmented matrix [A|I] using row operations.The Attempt at a Solution I just can't seem to get this one out, it's the last in a series of 9 similar questions and the first I am to have a hard time with. First few attempts involved...

Homework Statement several KVL equations combined I got till here [ 3+2i -1-(5/2)i 0 ] [I1] [ 10 ] | -1-5/2 3+3i -2+3i | [I2] | 0 | [ 0 -2 2-5i ] [I3] [ -3.5355 - j3.5355 ] where the Homework...

3x+3y+3z=3 x+y+z=-1 3 3 3 | 3 1 1 1 |-1 1 1 1 | 0 0 0 0 | 1 x = -y -z y = 1 Substitute y into x, x = -1 -z Let z = t, tER Then x = -1 -t, y = 1 The corresponding vector equation of the line intersection is: (x,y,z) = (-1, 1, 0) + t(-1, 0, 1) Does that look right...

Homework Statement Use row reduction to show that: [1 1 1] [a b c] = (b-a)(c-a)(c-b) [a^2 b^2 c^2] Homework Equations The Attempt at a Solution So I multiplied -a by row 1 and added it to row 2. I then multiplied -a^2 by row 1 and added...

Hey, I was looking for help on these questions dealing with row and column spaces... 1. Prove that the linear system Ax = b is consistent IFF the rank of (A|b) equals the rank of A. 2. Show that if A and B are nxn matrices, and N(A-B) = R^n, then A = B The first one I can't get much...

Ten deputies must be aligned on a bench. How many ways of doing that is there, provided that the russian deputy and the american deputy do not want to be placed side to side, and that the english and french ones want to be side to side. Since the english and the french deputies want to be side...

Problem: #29 in Strang Linear Algebra Prove that the identity matrix cannot be the product of 3 row exchanges (or five). It can be the product of 2 exchanges (or 4). Now, to start, we try to count the number of rows that are different from the identity matrix. For the first row exchange, it's...

http://www.guardian.co.uk/airlines/story/0,,1778038,00.html Yessss!

Hi Given A an n x n matrix where the columns are the set of standard vectors S = {e1, e2,...e_n} in R^n These vectors are orthonormal according to the definition since <e_i, e_j> = 0, i \neq j <e_i,e_i> = 1 Since the columns of A then they are orthonormal according to the...

I wrote this in September so that I could do matrix row reduction on my TI-89. It works, usually, but sometimes it doesn't row reduce all the way. Any ideas what I've done wrong? Or is it just some strange quirk of the calculator? If you don't know TI-89 code, it is self explanatory except...

Hello everyone, its me. I had a question again: I was suppose to determine if these vectors, A, B, and C, and D Linear Independant, Well A, B, C are linear independant, but D is not, I got D = 3/5 -4/5 -1/5 0 A = 1 0 0 0 B = 0 1 0 0 C = 0 0 1 0 I row reduced and got: 1 0 0 0 1 0 0 0 1...

Please don't say just practice. Any specific tips? In my class we're not allowed to use calculators, consequently I am spending all my time row reducing to find basis, dependence, etc. Frankly, I am just horrible at it, I just can't see how to get to the end. I am a bit perplexed on the...

Hello everyone... I have the following matrix: A = -1 -4 1 7 -9 0 10 3 -3 -9 1 2 I can't row reduce this sucker! This isn't an agumented matrix i don't think, so i can't just take the square matrix and then find the inverse and mutliply it by vector b to find the values of a, b, c, d; So...

Hello everyone, I would rather find the cofactors and find the determinant than row reducing this, but is it possible, its not square! But our teacher is acting like its possible, so it must be! here is the equations: x+y+z = 4 2x-y+4z=9 3y-z = 1 so i got: 1 1 1 4 2 -1 4 9 0 3 -z 1...

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...

I don't understand how one visualizes in row pictures of equations. There is an example in the book: With A=I(the identity matrix) 1x+0y+0z= 2 0x+1y+0z= 3 0x+0y+1z= 4 They drew these in the xyz plane. I don't know how they did this, can someone explain me that?

I am working with the following equation: |1 -2 3| |6 -11 15| |4 -14 21| a. add -4 time Row1 to Row 3 b. add -6 times Row 1 to Row 2 c. add 6 times Row 2 to Row 3 d. multiply row 3 by -1/9 I have come up with the following answer: |24 -48 72| |180...

My sister has horrible allergies which cause her to sneeze mulitiple times. Once she sneezed 36 times in a row! My question is why do we sneeze and why do some people sneeze a ridiculous number of times? Is it true that sneezing kills brain cells? Does it kill more brain cells if you hold it...