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). 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, P2 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 g has no solutions. (4b, Write the system of equations for part a) in matrix form Aa = b where a = (m, q)". (4c, Compute (AT A)–1.

Algebra for College Students
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Chapter8: Functions
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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).
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, P2 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 g has no solutions.
(4b,
Write the system of equations for part a) in matrix form Aa = b where = (m, q)".
(4с,
Compute (Aª A)-1.
(4d,
Compute :
(AT A)-1 A"b and find m = 1 and q = x2.
(4е,
Plot the line obtained by replacing m and q and the points P, P2 and P3
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). 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, P2 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 g has no solutions. (4b, Write the system of equations for part a) in matrix form Aa = b where = (m, q)". (4с, Compute (Aª A)-1. (4d, Compute : (AT A)-1 A"b and find m = 1 and q = x2. (4е, Plot the line obtained by replacing m and q and the points P, P2 and P3
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