Question

IPPOOH. 34. The following table shows the test scores of seven students on three tests. Test 1 Test 2 Test 3 Jones 90 | 75 60 Chan 70 Rocco 81 Johnson 72 Stein 63 Rio 87 69 Smith 50 77 | 83 View the columns in the body of the table as vectors ej, c2, and cz in R?, and view the rows in the body of the table as vectors ry, r2, ..., r, in R3. (a) Find scalars kj, k2, and kz such that the components of the vector x = kıcı + k2c2 + kzcz are the average test scores for the students.

Answer 1

The following table shows the test scores of seven students on three tests. Test 1 Test 2 Test 3 Jones 90 75 .60 • The columns in the body of the Chan 54 Rocco table are considered as vectors ć, į and the row are as vectors & R 8, 8, 85, 86, 8 Johnson 46 Stein Rio Smith 50 (a) The average score of Jones - 3 (90 +75+60) = 1.90 3.75 +4.60 Similarly, the average score of Chana 54 + 3.92+ +.70 the average score of smith = 3.50 ++ 3.777 3.83 The vector representing the average sco orest + دل نسبة الى سما (6) >> izgu, + :K, = 1/3, K₂=t, K2=t The average score of all the students in test 1= 1/2 150+54+63+70+96787+50) The average score of all the students in test 2 = + (75+92+70+717 90+72477) The average score of all the students in test 3 = 1/2 (60+70+81+72763+69+83) The vector representing the average scores 32(90,75,60)+'}(5492,70)+(63.70,80)+4(70,7179 +4(46.90,63)++(87, 7269)+4150,77,83) * = 77, + the + + 21 74 + 1 + is + + + 75

K = /1 162 271 kg = 2 kg = 2 ks = 12, k = 1 kg = 1 (C) * = £ G + t { + 1 2 3 = (G+ {+ 2 [g) = 16+1 Ęt 2 Ğ Š It means Hita the weightage of test 1 test 2, test 3 are respectively 1, 1 and 2.