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# Linear Algebra

### Complementary Angles and Systems of Equations

Two angles are complementary of each other. Twice one angle is equal to the other angle plus the product of three and five. A. Set up a system of linear equations to represent the two angles. (Hint: You will need two equations and two unknowns.) B. Graph each of the equations on one rectangular coordinate system. (Hint: Y

### Linear Operators : Finite-dimensional Vector Space, Fields and Mappings

Let V be a finite-dimensional vector space. The base field F may be either R or C here. Let T, an element of the linear mapping of V to V, L(V), be an operator. Suppose that all non-zero elements of V are eigenvectors for T. Show that T is a scalar multiple of the identity map, i.e., that there is a &#955; in the Reals such

### Consider the following data that show temperature

Consider the following data that show temperature of a 1,000 g sample of water at normal atmospheric pressure as a function of heat supplied. A kJ can simply be thought of a unit of heat. Temperature Heat Supplied 0 oC 0 kJ 10 oC 42 kJ 30 oC 126 kJ 50 oC 209 kJ 80 oC 335 kJ 99 oC 414 kJ 100 0C 420 kJ Base

### Linear Algebra : Change of Coordinates

If you let B = {v1, v2, ..., vk} be a basis of a subspace V of ; and you let Q = (qij) be an n x n matrix such that C = {Q(v1), Q(v2,)...,Q(vk)} is a basis of V. If , what are the coordinates of v with respect to B? Also, if what are the coordinates of Q(v) with respect to C? Please see the attached file for the fully f

### Systems of Equations Word Problems

Supppose a baseball is thrown at 85 miles per hour.The ball will travel 320 ft when hit by a bat swung at 50 miles per hour and will travel 440 ft when hit by a bat swung at 80 miles per hour. Let y be the number of ft traveled by the ball when hit by a bat swung at x miles per hour.(Note: The precceding data is valid for 50 les

### Linear Algebra : Linear Combinations

If you assume {v1, v2, ..., vk} and , and you also assume {v1, v2, ..., vk} are linearly independent and {v1, v2, ..., vk, w} are linearly dependent. How would you show that w can be uniquely expressed as a linear combination of {v1, v2, ..., vk}? Also, if the zero vector is included among the vectors {v1, v2, ..., vk}, w

### Systems of Equations Substitution and Addition Methods

Solve the following system by graphing: 14. x - 2y = -6 y = -3x/2 - 1 15. y < 5x - 2 y > 3x - 2 Solve the following systems by the addition method: 16. x + 2y = 4 3x - 6y = 6 17. 4x - 5y = 20 y = 4/5x - 4 Solve the following systems by the substitution method: 18. 7x - 4y = 26 y =

### Heating Water : Modeling with a Linear Equation

Water is the most importnt substance on Earth. One reason for its usefulness is that is exists as a liquid over a wide range of temp. In its liquid range, water absorbs or releases heat directly in proportion to its change in temp. Consider the following data that shows temp of a 1,000 g sampe of water at normal atmospheric pres

### Differential Equations : Lab Reports - Two Magnets and a Spring

Please do Lab 2.1 and Lab 4.1 in attached file.

### Matrices, Systems of Equations, Linear Programming, Simplex Method and Measures of Central Tendency

Please see the attached file for the fully formatted problems. ________________________________________ 1.) ________________________________________ 2.) Find the solution of the following system of linear equations: x + 2y - 7z = -1 3x + 7y - 24z = 6 x + 4y - 12z = 26 ______________________________

### Solutions to Systems of Linear Equations

Determine if the given ordered pair is a solution to the system: 12. 2x + y = 5 (4, -3) x - y = 1 22. 4x - y = -2 (-1, -2) 3x + y = -5 Solve each system of equations by the graphing method: 32. x - y = 4 x + y = 2 48. -4x + 4y = 4 y = x + 1 Solve each system of equations by the substitution

### Solve the equation by graphing.

These are questions that I got wrong on a test..can someone show me how to do these? ________ Solve the equation by graphing. 2x-3y=12 3y-2x=-12 is this equation independent inconsistent or dependent? __________________________________________ Solve the equation by graphing. 3x-y=4 3x-y=0 is this equation

### Systems of Linear Equations Differences

Please assist to understand the difference in these different methods. Please show work so I can follow the solution. Determine if the given ordered pair is a solution to the system: 12. 2x + y = 5 (4, -3) x - y = 1 22. 4x - y = -2 (-1, -2) 3x + y = -5 Solve each system of equations by the graphing method:

### Vector Cross Products and Vector Equations

Compute these vector quantities. 1) (i+3j-k) X (4i-j+2k) 2) (-i+3j+4k) X [(2i-j-k)x(i+j-3k)] Find the characteristic equation for the matrix below and determine its eigenvalues and the corresponding eigenvalues. -2 4 0 1 1 0 -3 4 3 Find the equations for the indicated geometrical objects: 1) the plane containing

### Systems of Equations and Inequalities and Absolute Values

How do you solve by the substituation method? x=y+3 3x-2y=4 would it be inconsistent, independent or dependent? ______________ word problem Ziggys famous yogurt blends regular yogurt that is 3% fat with its no-fat yogurt to obtain lowfat yogurt that os 1% fat. How many pounds of regular yogurt and how many pounds o

### Slope of a Linear Equation

What is the slope of 3x-2y=-1 ?

### Linear Equations and Graphs

Please show work so I can understand how to solve. Need assistance with the following word problems: A. Given the following linear equation: 2x - 5y = 5 a. Graph the line for the given equation. b. Derive an equation for a line parallel to the given line passing through the origin (0 ,0). c. Graph the second line.

### Linear Equations

Determine if the given ordered pair is a solution to the equation: 4. -3x + y = -2 (0,2) 6. 2x - y = -3 (-2, -1) Find the specified values: 8. 6x - 3y = 12 x-intercept & y-intercept 10. 4x - 2y = 6 slope & y-intercept Re-write the equations in the specified form: 12. y = 2x -3 write in standard form

### Questions about Systems of Equations

1. How do you interpret the solution of a system of equations by the corresponding graph? 2. Is there a basic difference between solving a system of equations by the algebraic method and the graphical method? Why? 3. Which method do you think is better for solving linear equations - addition or substit

### Ideals for Intersections

Please answer each part in full: Let I and J be ideals of R: (a) Prove that I+J is the smallest ideal of R containing both I and J; (b) Prove that IJ is an ideal contained in I (intersection) J (c) Give an example where IJ is not equal to I (intersection) J (d) Prove that if R is commutative and if I+J=R, then IJ

### Inequality and line equation

1.) The price of a personal computer is \$2000. The markup is \$150. What is the dealer cost? 2.) Solve the inequality 4y - 7 > 9y - 2. Use set-builder notation. 3.) Graph using slope and y-intercept method of y = (3/2)x - 3 4.) Graph using slope and y-intercept method of 5x + 5y = 10 5.) Graph the inequality

### Linear Equations and Solving Equations

The function that relates weight in grams of a crystal (w) to the temperature t in degrees Fahrenheit in which it was grown is as follows (fictitious): W(t) = 0.8t + 12 Find w(-6). a. impossible to tell from info given b. less than 8 grams c. at least 8 grams but less than 10 grams d. at least 10 grams but less t

### Why is it true that any two points satisfying a linear equation will give you the same graph for the line represented by the equation?

1. Why is it true that any two points satisfying a linear equation will give you the same graph for the line represented by the equation? 2. How do you interpret the slope and y intercept in a real world case? 3. By looking at two linear equations, how can you tell that the corresponding lines are pa

### Systems of Equations with Three Variables and Real-Life Applications

Hello again ! trying to solve for x and Y in the following problems. please explain 1. a. X + Y=6 ; 2X + Y =8 b. 7X + 3Y=14 ; 5X + 9Y= 10 c. 4X + Y= 16 ; 2X + 3Y= 24 d. 12X + Y= 25 ; 8X - 2Y= 14 2. Suppose Bob owns 8000 shares of company X and 6000 shares of Company Y. The total value of Bobs holding of these

### MATLAB Signals Theory- Linear Time - Inveriant Discrete Time System

A linear time-invariant discrete-time system has transfer function h(z)=((z^2)-z-2)/((z^2) + 1.5z-1) a. Use MATLAB to obtain the poles of the system. Is the system stable? Explain. b. Compute the step response. This should be done analytically, but you can use MATLAB commands like conv and residue. c. Plot the first seve

### Differential Equations : Bifurcations in Linear Systems

In Chapter 3, we have studied techniques for solving linear systems. Given the coefficient matrix for the system, we can use these techniques to classify the system, describe the qualitative behavior of solutions, and give a formula for the general solution. In this lab we consider a two-parameter family of linear systems. The g

### Solving Systems of Equations

1. Solve each system by graphing. y = - 2/3 x 2x + 3y = 5 2. Solve each system by the substitution method. Determine whether the equations are independent, dependent, or inconsistent. 2x - y = 4 2x - y = 3 3. Write a system of two equations in two unknowns for each problem. Solve each system by substation.

### MATLAB Signals - Conv and Transfer Function of System

1. A discrete-time system has the following unit-pulse response: h[n] = 0.5^n - 0.25^n for n >= 0 Correspondingly, the following difference equation describes the behavior of the system: y[n + 2] - 0.75y[n +1] + 0.125y[n] = 0.25x[n +1] a. Use the MATLAB command conv to calculate the response of the system to a unit ste

### Systems of Linear Equations and Inequalities

I am at a total loss on these. Any assistance you could give me would be greatly appreciated. I have a total of 9 problems. Thanks a lot!! The start-up cost for producing widgets is \$449, and each widget costs \$91 to produce. What is the equation for this situation? Use X for # widgets produced and Y for cost. a. none of

### Acute, Obtuse, Right or Straight Angles.

1. Along a straight shoreline, two lighthouses, A and B, are located 2000 feet apart. A buoy lies in view of both lighthouses, with angles 1, 2, and 3 as indicated. (Angle 1 is denoted by , angle 2 is denoted by , and angle 3 is denoted by .) A. By looking at the picture, do you think is an acute, obtuse, right, or a st