Linear equations Definition and 233 Threads

Let b be the vector such that B = [A b] , and let a1, a2, a3 and a4 be the columns of A. Let m be the number of linearly independent columns of A, let k be the number of parameters (free variables), and let n be the total number of columns in A. In our example above, n = 4. Do you suppose...

This is a pretty basic question, but I just want to make sure. The question is to find the least square solution for \newcommand{\colv}[2] {\left(\begin{array}{c} #1 \\ #2 \end{array}\right)} \left( \begin{array}{cc} 1 & 2\\ 2 & 4 \end{array} \right) x = \colv{2}{2} I can just find...

Homework Statement solve 3^x = 11-x Homework Equations I attempted by drawing both graphs but I am searching for answers through algebra manipulation. The Attempt at a Solution x lg 3 = lg (11-x) x = [ lg (11-x) ]/[ lg 3 ] Any suggestions or solutions?:confused: Suggestions...

Ok i have a problem that i just can't solve.:frown: It says: sam has collected fifty baseball cards. The Major league baseball cards are worth $3.50 and the minor leagure baseball cards are worth $2.00 each. sam`s collection is worth $122.50 Q: Write a system of equations that can be used...

Homework Statement we have a tank with 400L of water with Cl, 0.02kg of Cl. Fresh water is pumped in at 4L/s and out at 10L/s. Find the amount of Cl in the tank as a function of t. Homework Equations Use of differential equations The Attempt at a Solution I set up V(t)=400-6t in...

Homework Statement is every system of 6 equations and 5 unknowns consistent? I think that not every one is consistent because after Gaussian elimination you may arrive at equation where 0=1, but I want a sure confirmation. Thanks

Homework Statement I'm told that this is a linear equation y' = \frac{4ln|x| - 2x^2y}{x^3} 2. The attempt at a solution x^3 = (4ln|x|-2x^2y)\frac{dx}{dy} giving: P = 4ln|x|-2x^2 Q = x^3 \int Pdx = 4x-\frac{2x^3}{3} e^\int^p^d^x = e^4^x^-^\frac^{2x^3}^{3} ye^\int^p^d^x = \int...

Howdy, I got down Cramer's rule down fine, now I need to extend it to include equations that have complex coefficients. Do I let each matrix entry be something like, "5 + 2i" or is there something more than that? For example, say we have (2+3i)x + (5+3i)y + (9-6i)z = 10 + i (4+3i)x + (5-3i)y...

we have the system a_i1x+a_i2y+a_i3z=b_i i=1,2,3 and we are given that it has a unique solution (1,2,0) i need to find the set of solutions for the next system: a_i1x+b_iy+a_i3z=a_i2 what i did is: we have the solution for the first equation then we have a_i1+2a_i2=b_i so we put it in the...

I need some help on finding the general solution. I can find the complimentary solution, I'm having trouble finding the particular solution. Can anyone give me any tips. y"+9y=t^2e^(3t)+6 y"-2y'-3y=-3te^-t y"+2y'=3+4sin(2t)

Could someone please explain how to graph y=x-2 and y=4-x and find the coordinates of the point of intersection.

Does anyone know how to write a linear equation in Mathcad. Example 5.6=22x/(x+22) I am using an older version and it does not like the unknown variable.

Hi, I am finding some of this confusing, can someone explain this? so I undersand that xy' + y = (xy)' lets say that I have 2ty' + 4y = 2t^3, what is (xy)'? would it just become d/dx(2ty) = 2t^3?

A while back in maths we were introduced to the linear equation in two forms: a x + b y = c (1) y = m x + c (2) Now I can use both forms of these, but I was told that: y = m x + c \Leftrightarrow a x + b y = c where m = \frac{a}{b} Thiis can't be right can it? As: a x + b y = c b...

I have an example and a problem i am working on. The example is as follows: There are three strings. One hangs down with 100N while of the other two one goes up to the right from the equilibrium point at 45 degrees and the other goes left. I believe this set of Rx and Ry vector components is...

"Show that the number of distinct solutions of a system of linear equations (any number of equations and unknowns) over a field Z_p is either 0, or a power of p." I don't know where to start. Suppose there are n unknowns, if only I can show that the solution space is a subspace of Z_p ^n...

For my first year formal lab I am having a little bit of trouble with one aspect, let's see if anyone can help Im trying to rearrange the equation T = 2pi [(32 L I)/(pi S d^4)]^1/2 ...(sorry, i don't know how to use the better way of displaying math) to form a linear equation so it can...

Find/solve following system of linear equations, 3y_1 + 2y_2 +y_4 = 6 5y_1 - 2y_2 +2y_4 = 5 -2y_1 + y_2 - y_4 = -2 WORK DONE : I am told that the answers are y_1 = 1 and y_2= 1 and y_4 = 1. But i don't understand how to obtain these values... I know how to solve 2 linear...

I can not, for the life of me, figure out how to set the following up into a system of equations. An object composed of x gram-mole of lead (specific gravity 11) and y gram-mole of tin(specific gravity 7) weights 82 gram-moles in air and 77 gram-moles in oil of specific gravity of 1/2. Find x...

The question asks: Find the equation of the plane that passes throug the points (1,2,3), (3,-1,3), and (5,0,7). (Hint: Recall that the general equation of a plane is ax + by +cz =d.) You could make 2 vectors with those three points then find the normal by taking the cross product of those two...

Hi, This is the problem: Lorraine has $7.70 in dimes and quarters. If the number of quarters is two more than twice the number of dimes, how many of each type does she have? I know the answer is 12 dimes and 26 quarters by figuring it in my head, but my professor requires us to show work to...

I'm reading through the book "Linear Algebra", by Jim Hefferon (which you can download for free!). In section I.3, he describes that the pattern of solutions for a system of linear equations: "They have a vector that is a particular solution of the system added to an unrestrictred combination...

I'm hoping someone can come along and give me a tap on the head for being so silly, but I've been trying this problem *all day* and i just can't seem to get a correct answer, even when checked with other people, we're all stumped! What we have: 3x - 2y + 5z = 0 x + y + 5z = 5 x - 2y - z =...

It won't work and I don't see what I'm doing wrong. Find the solutions of the following system of linear equations: x + 3y - z = 1 2x + y + 2z = 3 5x + z = 2 I put these into the form Ax = b, where A = (1 3 -1) (2 1 2 ) (5 0 1 ) x = (x) (y)...

Problem Prove that, where a, b, c, d, e are real numbers and a <> 0, if ax + by = c has the same solution set as ax + dy = e, then they are the same equation. Given Solution If a <> 0 then solution set of the first equation is {(x,y) | x = (c - by)/a}. Taking y = 0 gives the solution (c/a...

Hi I have obtain two third degree polynomials p and q which are determint by the following conditions: p(-1) = 1 , p'(-1) = 0 q(1) = 3 , q'(1) = 0 p(0) = q(0) , p'(0) = q'(0) where p = a_1 * x^3 + b_1 *x^2 + c_1 *x + d_1 q = a_2 * x^3 + b_2 *x^2 + c_2 *x + d_2...

I guess i didn't get the last one completely because I've been having a hard time with this one. Solve 3x + iy + (2+i)z = 3i -ix + y + z = 1 x + y + (2+i)z = i i've tried dividing through by the leading coefficent, and re-arranging it...but can't seem to get the right answer...

Find the solution in C to the following linear system of equations. (a) (1-i)z + 4w = 2 + 8i (b) 3z + (1+i)w = 1 + 5i I tried expanding but that didn't get me anywhere. Then i put it in a matrix, but i didn't know how to go from there. Any suggestions? Thanks.

A certain manufacturing plant burns fossil fuel in its manufacturing process. The fuel that is obtains can be divided into 3 types - low emmission fuel, moderate emmission fuel and high emmission fuel. Federal law requires that high emmission fuel be discarded and that the company can burn at...

I haven't done this in a long time so please bare with me. I need to solve this system to find the percent abundance of 2 isotopes. 68.9257x + 70.9249y=69.723 x+y=1 In order to solve the system by addition/subraction one would multiply 68.9257 through the second equation, then procede...

I would like to know if anyone of you can help me simplify the main ideas of the Simplex method used to optimize a function...Would you please help me ? In case which I don't use Simplex to solve the problem, could you tell me if there exist to be any other methods that I can choose ...

I hope some can help me here. What is the best strategy in solving 4 linear equations with five unknown variables?

what is M? x1+x2=2x3+4x4=5 2x1+2x2=3x3+x4=3 3x1+3x2-4x3-2x4=1 why does M={ 1 1 -2 4 5 } 2 2 -3 1 3 3 3 -4 -2 1 i know how they got this but how do you get ~{ 1 1 -2 4 5 } { 1 1 0 -10 -9 0...