Matrices & Determinants Questions and Answers

Find the matrix A of the linear transformation T R R given by C T 471 22 8 23 6a 9 23

or each of the matrices M listed below find a sequence of elementary matrices E1 E M is in echelon form Show your work step by step b 1 point M 1 2 1 0 1 Ep such that the produc

ACT PREP MATH PART ACT Question 4 of 60 The determinant of matrix A is shown below Consider matrix B If x 2 and y 3 then what is the determinant of matrix B 89 65 O 77 O65 O 89 Nex Reset B A a b cd ad 2x 3 5 32 bo 4y 5y

20 Find the area of the kite 15 15 9 CK 12 12 16 20 20

19 9m 12m 4 m 9m m 9am 4 m1 am 4 m 1 21 35m 230n 400 23 25v 20v 4 4 1 4 4 1 2 2 20 20a 4a 28 22 16r 24r 9 24 25n 60n 35

Use Gauss Jordan elimination to solve the linear system and determine whether the system has a unique solution no solution or infinitely many solutions If the system has infinitely many solutions describe the solution as an ordered triple involving a free variable Select the correct choice below and fill in any answer boxes within your choice OA There is one solution The solution is D Type an exact answer in simplified form x y Z x 5y 5z 5x y 11z OB There are infinitely many solutions The solutions are 2 where z is any real number Type an exact answer in simplified form OC There is no solution 4 15

Surface Area in Round to the nearest hundredth as needed Volume in Round to the nearest hundredth as needed Find the surface area and volume of the solid Use 3 42

1 1 C In R a find the orthonormal basis by Gram Schmidt Method 35 point

Solve the system using row operations 3u If your answer includes any arbitrary parameters name them s1 s2 etc as needed u v w x 60 U w X 10x 7w 3w 13 13

For the function g x 2 x 4 2 8 answer parts a through c a Graph g x 2 x 4 2 8 Use the graphing tool to graph the function b Determine the domain and range of the function The domain is 00 00 Type your answer in interval notation The range is 0 8 Type your answer in interval notation c Determine where the function is increasing and where it is decreasing Determine where the function is increasing Select the correct choice below and if necessary fill in the answer box to complete your choice 2 OA The function is increasing on the interval Type your answer in interval notation B The function is never increasing CID

Function is represented by f x x 2 Another function g x has the following table of values I 1 1 0 g x 0 4 3 6 10 2 3 What is the average rate of change for f x and g x over the interval x 0 tox 3 and which function has the grea average rate of change O The average rate of change from x 0 to 2 3 for f x is O The average rate of change from z 0 to z 3 for f x is O The average rate of change from x 0 to x 3 for f x is and for g x is and for g x is f x has the greater average rate of change g x has the greater average rate of change and for g x is 2 f x has the greater average rate of change

Given the piecewise function above evaluate the following statements write DNE if the limit does not exist lim f x 24 1 lim f x 2 0 lim f x f 1 lim f x 2 2 lim f x 846

2 Elimination 4x 2y 12 4x 8y 24

6 The graph of y k sin X is shown below for unknown constant k What is the x coordinate of point A 4 shown marked on the diagram 1 7k 6 5k 2 3 8 4 10 y M full by the equation V 55 cos A at maximum 7 The volume of water V in a storage tank can be modeled as a function of the number of hours since it was 77 t 67 where V represents the number of gallons of water in the tank Which of the following represents the maximum number of gallons 1 74 3 105 2 96 4 122

Determine whether this pair of lin 5 9x 3y 3x 9y 1

Use elementary row operation to solve the system EEB 3x 2y B 3 z Find the value s for 3 for which the system has no solution T Y 8 1 2

1 The following two system of equations are equivalent 2x 2y X y 3x 4y True False True False x X 2 The general solution to the following system has 1 parameter 2y 6z y 4z 2y 5z X y 2y 2z III 0 4 7 4z 6z 4w 2w 4w 177 3 Given a 3 x 4 augmented matrix R 3R R3 is an elementary row operation True

The graph of a cosine function shows a reflection over the x axis an amplitude of 5 a period of 6 and a phase shift of 0 25 to the right Which is the equation of the function described of x 5 cos 3mx 4 of x 5 cos Of x 5 cos Of 2 5 cos

The graph of y 5 cos CHES is obtained by shifting the graph of y cos x units horizontally to the stretching e vertically by a factor of and then shifting units can

Use the algorithm for finding A to find the inverses of the matrices shown to the right Let A be the corresponding nxn matrix and let B be its inverse Guess the form of B and then show that AB I 900 990 999 0 9000 9900 9990 0 0 0 9 0 Type an integer or simplified fraction for each matrix element 99 COS 900 990 and 999 900 990 999 999

Solving Systems of Linear lations olve the system of equations graphically If the systen ngle ordered pair as a solution state whether the sys ependent x 3 y 3x 3

The entire graph of the function h is shown in the figure below Write the domain and range of h using interval notation a domain b range UE 0 0 0 0 0 0 0 0 Q nun DVD

Points A B and C are three vertices of a rectangle Complete

Find a SVD for the following matrix 1 2 2 C 1 2 Show Transcribed Text Which of the following is VT S 3 C 1 1 47 1 1 11

Which of the following are valid equations for the line parallel to the y axis and passing through the point 0 H t1 0 0 A B 0 t 1 8 0 1 t1

point Find the angle a in radians between the vectors N and

Move the slider h so that the graph of y f x in the answer box 3 T gets shifted to the right 3 units Then type the new 2 2 f x x h 0 00 T Don t forget to shift the graph to the right Using function notation i e f x enter the function that results from the transformation

consider the points P 0 0 1 Q 1 0 2 R 3 3 2 and let A be the area of triangle PQR Select the correct interval for A a A 2 b 2 A 4 c 4 A 6 d 6 A 8 e A 8

Find IAI IBI A B and IA BI Then verify that A B A Bl 0 1 3 0 1 1 1 1 0 3 1 1 3 1 1 0 1 A a A 11 b B 6 c A B 0 4 3 2 0 2 B 4 1 2 2 11

Sketch a graph of f x 5 4 3 2 1 Clear All Draw 5 4 3 2 1 1 2 3 4 10 3 if x 1 2x1 1 1 2 if 1 x 2 if x 2 3 4 16

Graph the system below and write its solution 2x y 2 y x Note that you can also answer No solution or Infinitely 10 8 y

Solve the equation Separate solutions using a comma DOT NOT use spaces in your solution x 5 3x 2 0

11 Problem 2 3 2 28 Find a basis for the image of the matrix A 1 2 5

matrix to reduced row echelon form A 3 2 1 3 1 0 9 21

Dotermine the slope of the line throu

Find an LU factorization of the matrix A with L unit lower triangular A L U 11 4 0 82 1 8 12 33 3

Solve the equation Ax b by using the LU factorization given for A Also solve Ax b by ordinary row reduction 1 1 A y 2 6 3 X 2 2 6 9 7 3 00 10 3 1 Let Ly b and Ux y Solve for x and y 2 6 3 3 1 0 0 1 0 b 4 18

Suppose that the augmented matrix of a system of linear equations for unknowns x y an 10 11 4 1 2 11 2 The system has 001 Solve the system and provide the information requested a unique solution which is 1 4 two of which are 1 2 X infinitely many solutions x x 0 0 y 0 y 11 y 0 N z Z 3 X

The following table shows the results of a survey of 100 authors by a publishing company Established Authors Total 33 67 23 100 Compute the relative frequency of the given event if an author as specified is chosen at random An unsuccessful author is established Successful Unsuccessful New Authors Total 8 25 52 77

8 a Show that relative to the xyz coordinate system in R the nullspace of A is all the points on the z axis and the the column space is all points in the xy plane A 0 1 1 0 0 0 b Find a matrix whose null space is the x axis and whose column space is the yz plane c Find a matrix whose null space is the y axis and whose column space is the xz plane

4 Solve this multivariate 4x 3y 2z 52 2y 3z 3z x Y x system by Gaussian elimination 33 4 26 3 1 1 2

n det t def ghi gh hi a b c a de f g b h 3 find the following determinants 9d a 9e b 9f c C i 9d a 9e b 9f c

A solid right square prism is cut into 5 equal pieces parallel to its bases The oolume of each piece is V 1 5 s 2 h Solve the formula for s

State the domain and range of each function Explain your thinking a f x 3 2x 8 1 4 marks b g x 5 cos 9 x 80 3 3 marks c 2log x 5 1 4 marks

5 Newly acquired autos only qualify for liability coverage from the date of purchase until the vehicle is added to an existing auto policy A True B False

Given A 2 3 3 Express 4 and A as a product of elementary matrices EM A

the given graph 6 5 4 3 2 1 5 4 3 2 1 1 D4 6 y 2 3 2 3 4 5 6 X

Geppetto is a puppet maker He starts the month with 5 puppets ready to sell and makes 9 puppets per day Write an equation to model this situation used for days and p for puppets Preview

Sketch a graph of y x 2 2 Steps for drawing your graph Step 1 Click on the shape below graph that you want to draw Step 2 Click on first point that is part of your graph Step 3 Move mouse to second point that is part of your graph and click on it 5 4 5 4 3 2 1 3 2 1 1 2 3 4 1 2 3 4 cit 5

Practice Given each inequality and a set of possible solutions determine which values are solutions of each inequality Examples 1 and 2 1 12 t 7 19 18 17 2 h 4 2 1 1 2 3 7 a 10 4 3 2 5 8r48 4 5 6 7 4 4 3 2 ONLINE 4 18 15 d 2 3 4 6 15 23 40 45 50 8 18 2c 8 9 10