Linear Algebra Questions and Answers

Mr Young built a greenhouse 42 feet wide 110 feet long 5 feet to the eaves and 14 feet to the ridge cap How many square feet of plastic does it take to enclose the greenhouse

Task 1 Modelling a real world situation You have been asked to sell tickets to a charity event You know that as the price of the ticket increases there will be less people who are able to attend Your task is to come up with the equation which would best model the ticket price in compared to the revenue Let x represent the price of the ticket and y represent the revenue in you would be able to raise for charity Unit Price 5 Profit 11250 10 12000 15 12250 20 12000 25 11250 30 10000 35 8250 6000 3250 40 45 a Copy the table and graph the points you see and include the line of the best fit You may use the graphing software to help you have to adjust this after you have completed task 2

Consider the function f x ax2 bx c The graph of y f x is shown in the diagram The vertex of the graph has coordinates 0 5 12 5 The graph intersects the x axis at two points 2 0 and p 0 diagram not to scale 2 0 p 0 10

A player throws a basketball The height of the basketball is modelled by h t 4 75t2 8 75t 1 5 t 0 where h is the height of the basketball above the ground in metres and t is the time in seconds after it was thrown a b Find how long it takes for the basketball to reach its maximum height 6 909 maximum Assuming that no player catches the basketball find how long it would take for the basketball to hit the ground Another player catches the basketball when it is at a height of 1 2 metres 1 2 4 75 t 8 75 1 5 9 bns 0 c Find the value of t when this player catches the basketball U 20 9

plane Two children are playing with a ball The girl throws the ball to the boy The ball travels in the air curves 3 m to the right and falls 5 m away from the girl as shown in Figure 5 46 If the plane that contains the trajectory of the ball is perpendicular to the ground find its equation 5m 3m

Which point represents the opposite of 11 b d 3 2 1 0 1 2 3 O a Ob Oc d

1 Let T R Rm be a linear transformation a If T is injective what can you determine about the relationship between m and n If T is surjective what can you determine about the relationship between m and n Make sure to briefly explain your answers b Let L Rm Rk be another linear transformation Prove that the composition LoT R RA L T is a linear transformation Clearly indicate where you use defined by LoT 7 linearity of L and T

3 4 cm ekil 3 ekil 1 ekil 2 Kenar uzunlu u 5a cm olan kare eklindeki bir ka t nce ekil 1 deki gibi yatay do rultuda daha sonra ekil 2 del gibi dikey do rultuda olacak ekilde ortadan ikiye katlanm t r Son olarak bu ka ttan ekil 3 teki gibi bir kenar uzunlu u 4 cm olan kare eklindeki bir par a kesilerek kar lm ve geriye kalan k s m katlama yerlerinden tekrar a lm t r Buna g re son durumda bu ka d n santimetrekare cinsinden bir y z n n alan na kar l k gelen cebirsel ifade a a dakilerden hangisi ile zde tir A 25a 16 B 25a 64 C 25a 16 D 25a 64

Graph y 2x 5 9 8 7 6 5 4 3 2 6 Y 8 7 64 5 4 3 2 3 1 2 3 4 5 6 7 8 9

Instructions Write your answers neatly on blank sheet s of paper and upload your solutions to Grade scope You may also write your solutions on a tablet When submitting to Gradescope you must indicate where each question appears in your solution If you do not have a solution to a question then write no solution for that question on your paper Leave all final numerical answers exact unless otherwise specified Show your steps work Box or circle your final answer 1 Suppose A is an m x n matrix such that the equation AF 6 has a solution for every bRm a If m n what if anything can you determine about the linear dependence independence of the columns of A b If m n what if anything can you determine about the linear dependence independence of the columns of A c Is it possible that m n You must justify each answer you may use theorems stated in class 2 Suppose a linear transformation T R2 R satisfies Determine T ED T H B and T 2

Assignment Quad Form Practice Math 2 What Is a Metaphor Solve each equation below using the quadratic formula Cross out the box that contains the solution set Whe you finish print the letters of the remaining boxes in the spaces at the bottom of the page 1 x 4x 3 0 X 1 the yo 1 X 42 6 16 3 x 5 6 0 5 x 2x 8 0 Date 225 2 x 7x 10 0 4 x 3x 4 0 6 r 5x 2 0

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