# linear

1. ### Linear Quadratic Systems Help

Determine the restrictions on the y-intercept so that y = 3x^2 + 6x - 1 intersects with a line with slope 2 in more than one place. I equate the problem like how it was shown in my lesson and made an equation for slope 2 y = 3x^2 +6x -1 (Quadratic Equation) y = 2x + b (Linear Equation) 3x^2 + 6x...
2. ### Independent v.s. dependent columns

Hi, I'm lost with this image: Can someone please explain the description of Figure 4.7? How is a1, a2, and a3 not in a plane while c1, c2, and c3 in the same plane? I struggling to find the reasoning behind this. (Sorry I forgot to convert the "1" in "a1" and the "2" and "a2" etc as...
3. ### Linear Algebra: help with inner product space

I don't understand how to solve this type of problems and I can't find solved examples anywhere in my textbook or the internet. Can you help me out? In R^3 it's given the symmetric, bilinear form F: R^{3}\times R^{3}\rightarrow R : F((x_{1},y_{1},z_{1}),(x_{2},y_{2},z_{2})) = 3...
4. ### Word Problem: Systems of Linear Equations

Hi all, I have been trying to solve the following word problem for a few hours now. I think it's time to step in and ask for help after exhausting all of my resources to no avail. Three siblings Tommy, Susie, and Roland are 42 years old together now. When Susie was of Tommy's age, Roland was...
5. ### Linear algebra Gauss-jordan elimination problem

Hi. I've been working on this problem. Show that the following non-linear system has 18 solutions if { 0 <= a, b, c <= pi } sin(a) + 2cos(b) + 3tan(c) = 0 2sin(a) + 5cos(b) +3tan(c) = 0 -sin(a) - 5cos(b) + 5tan(c) = 0 So I substituted sin(a), cos(b), and tan(c) for x, y, and z and then used...
6. ### Complex linear integration

Hi everyone i need some help on some complex integration. I am struggling on how to go about these two questions as its a non-simple integral and we haven't covered this properly in Uni yet. On Question 3 i think I just have to present two options on whether z = w is included in C or not but...
7. ### linear Independence

linear Independence of Following
8. ### A simple question: can a linear transformation have the same matrix in different base

Hi: can a linear transformation have the same matrix in different bases? I have spent a whole evening trying to figure out whether this can be to no use. What is certain is that given a base, I can define a linear ttransformation by giving it's values over a base. That is, there exists a...
9. ### linear combinations

Can anyone help me solve this problem? It's from the first chapter of Strang. Solve to find a combination of the columns that equal b: \begin{aligned} u-v-w=b_1 \\ v+w=b_2 \\ w=b_3 \end{aligned} I tried doing some substitution, u,v and w's for b's but I ended up in a tangled mess with no...
10. ### Model Ratio using Linear Regression

Hello, I have a question about linear regression modeling on ratio. The original model with dependent variable of ratio is Y= (Y1/ Y2). Both Y1 and Y2 are dollar amount represent sales and balance respectively. The dependent variable Y is a continuous variable between 0 and 1. The equation...
11. ### Solve each system of linear equations

Hi, Please, solve each system of linear equations: x - y + z = 6 -x + y + z = 3 -x - y - z = 0 And questions 23, 25 and 29 Thanks)
12. ### Linear Regression Equations

Hi guys im using Open Office to try to solve math problems and i find its not working for linear equations. That above is the data ive entered into my open office when I try to tun LINEST function or use a t 83 graphing calculator to find the regression equation, I am completely unable to do...
13. ### determine whether the equation is linear or not

the answer is yes , and the ans is y = A(x+1) , how to get the ans ? i could only get dy/dx = y / (x+1) anyone can help ?
14. ### Linear Transformation Question

Hi, I need to write the matrix that represents the following linear transformation of the plane and then draw the image in quadrant 1. ...The transformation T(x,y)=(2x+6y, x+3y) The matrix I got was: 2 6 1 3 This led to reference points: O(0,0) - O'(0,0) P(1,0) - P'(2,1) Q(1,1) -...
15. ### Matrix linear system question

I have the following question and I have no idea where to start. It is broken into part a) and b). Part b) asks to find the row operations which I know how to do. The issue is I can't do part a) which asks to find 3 linear equations. I need these to form a matrix to do the row operations in part...
16. ### Matrix representing composition of linear transformations

Could someone check these for me please and point out where needs improvement? Thanks in advance! \text{Prove that T is a linear transformation or show it isn't by use of a specific counter-example. If T is a linear transformation, find its associated matrix.} a.) T_{a} \begin{bmatrix}x \\...
17. ### Linear Programming in AMPL

Hope this is the right thread. I've only just started learning AMPL but I'm stuck trying to figure out how to write a program that would solve this LP: Jimbo Enterprises produces n products. Each product can be produced in one of m machines. Let tij be the time in hours needed to...
18. ### Linear functions: Perpendicular lines.

Hey i need help with number 14 and 15. I know that the slope has to be -1 in order for the line to perpendicular.
19. ### Linear Programming problems.

Hello everyone. I'm flummoxed about how to formulate the linear programming problem for this questions, and was wondering if anyone had any ideas or hints on how to proceed with it? Any help would be greatly appreciated.
20. ### Linear functions

Hey everyone. Im having trouble with some homework on functions. For Number 5 c,d, how would i go about pluging those into the function? number 6 i dont understand what numbers to use and i dont know how to find the equation. hope i made sense ith my questions. :S