Matrix - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

Download Matrix - Linear Algebra - Quiz Solution and more Exercises Linear Algebra in PDF only on Docsity!

a f Math 205A Quiz 01 page 1 September 12, 2008 NAME Sunaected fon wg + 32, =p 1. Consider the system of equations a+ 5%. +3%3 + Try =t 202, + 100r2 + 62%3 + 14624 = w, where p, ¢, and w are three real numbers whose values we don’t know. 1A. What is the augmented matrix for this system? oO 0 { 3 P I 5 3 A t zo /00 G2 Ne |w 1B, By hand, find the matrix in RREF which is row equivalent to the answer in (1A). Show and label all your steps as we've done in class, for example, if you add 4 copies of raw 5 to row 8, write “rg — rg + 4rs”; if you swap rows 4 and 5, write “swap ry and rs”, etc. (you don’t need the quotes) Use steps that make the work easy; avoid fractions if possible. Note well that your column with p, ¢, and w will change as you change the coefficient side of the matrix. ° 3 P. @ . gg Gey ung ° ; ar oes = ee i GG 2G 10 joo 62 Mo | ee es wo) s he 756 be oem tne TL accyptik CO [ 3 P = tis ansuer CO co © w-20é “ep HOWEVER » if wW-1ok ~ tp #0 1C. Use the answer to (1B) to determine what relationship p, ¢, and w must satisfy in order for this system to have a solution. thin 10 The Original Si yates pea e) & Consiten€ hee 49 : Pi last ati mut. be. Z. ind Mut be OF ; Aus (04, Wires é more kpc ¢ t- Sel hr -b-d, (on Ie Fis Ml i REG PS eos dui os “Ee wW-19t-2p