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.
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
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.CT: Test
Problem 19CT
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