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Consider the relation between hours of study and quiz grade for three different students. (i) Student 1 did not spend any time and received 5 in the quiz. P = (0, 5) %3D (ii) Student 2 spent an hour studying and received 5 in the quiz. P = (1, 5) (iii) Student 3 spent two hours studying and received 8 in the quiz. P3 = (2, 8). We want to find a linear relation between hours of study and grade of the quiz y = mx + q where m and q are our unknowns, x represents the hours studied for the quiz and y the quiz grade. (4a Show that there is no line y = mx + q that passes through P , P and P3 using an inconsistent system of equations. Hint: Substitute the x and y values of P, P2, P3 in the line equation and show that the 3x2 system with unknowns m and q has no solutions. (4b Write the system of equations for part a) in matrix form Ax b where i = (m, q)" . (4c Compute (AT A)-1.

Consider the relation between hours of study and quiz grade for three different students. (i) Student 1 did not spend any time and received 5 in the quiz. P = (0, 5) %3D (ii) Student 2 spent an hour studying and received 5 in the quiz. P = (1, 5) (iii) Student 3 spent two hours studying and received 8 in the quiz. P3 = (2, 8). We want to find a linear relation between hours of study and grade of the quiz y = mx + q where m and q are our unknowns, x represents the hours studied for the quiz and y the quiz grade. (4a Show that there is no line y = mx + q that passes through P , P and P3 using an inconsistent system of equations. Hint: Substitute the x and y values of P, P2, P3 in the line equation and show that the 3x2 system with unknowns m and q has no solutions. (4b Write the system of equations for part a) in matrix form Ax b where i = (m, q)" . (4c Compute (AT A)-1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the relation between hours of study and quiz grade for three different students. (i) Student 1 did not spend any time and received 5 in the quiz. P¡ = (0, 5) (ii) Student 2 spent an hour studying and received 5 in the quiz. P2 = (1, 5) (iii) Student 3 spent two hours studying and received 8 in the quiz. P3 : (2, 8). %3| We want to find a linear relation between hours of study and grade of the quiz y = mx + q where m and q are our unknowns, x represents the hours studied for the quiz and y the quiz grade. (4а Show that there is no line y = mx + q that passes through P , P and P3 using an inconsistent system of equations. Hint: Substitute the x and y values of P, P, P3 in the line equation and show that the 3x2 system with unknowns m and g has no solutions. (4b Write the system of equations for part a) in matrix form Aš b where i = (m, q)" . (4c Compute (AT A)-1. (4d Compute i (AT A)-' A™ b and find m = x1 and q = x2. (4e Plot the line obtained by replacing m and q and the points P , P2 and P3 Optional - What do you observe? In what way is this line a good representative of the data.
Transcribed Image Text:Consider the relation between hours of study and quiz grade for three different students. (i) Student 1 did not spend any time and received 5 in the quiz. P¡ = (0, 5) (ii) Student 2 spent an hour studying and received 5 in the quiz. P2 = (1, 5) (iii) Student 3 spent two hours studying and received 8 in the quiz. P3 : (2, 8). %3| We want to find a linear relation between hours of study and grade of the quiz y = mx + q where m and q are our unknowns, x represents the hours studied for the quiz and y the quiz grade. (4а Show that there is no line y = mx + q that passes through P , P and P3 using an inconsistent system of equations. Hint: Substitute the x and y values of P, P, P3 in the line equation and show that the 3x2 system with unknowns m and g has no solutions. (4b Write the system of equations for part a) in matrix form Aš b where i = (m, q)" . (4c Compute (AT A)-1. (4d Compute i (AT A)-' A™ b and find m = x1 and q = x2. (4e Plot the line obtained by replacing m and q and the points P , P2 and P3 Optional - What do you observe? In what way is this line a good representative of the data.
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