Matrices & Determinants Questions and Answers

Let f x 5x 4 and g x x x 3 Perform the function operation and then find the domain f x g x f x g x Simplify your answer

From below options select the only elementary matrix O To 0 1 0 E 0 1 500 0 17 1 0 100 To E 0 To 0 17 E 1 0 0 C

Given A and b to the right write the augmented matrix for the linear system that corresponds to the matrix equation Ax b Then solve the system and write the solution as a vector Write the augmented matrix for the linear system that corresponds to the matrix equation Ax b Solve the system and write the solution as a vector X 2 A SO 3 4 4 7 4 7 3 b 15 45 36

Graph the following function y 1 sin Step 2 of 2 Determine how the general shape results on the axes provided Answer

Find the volume of a pyramid with height 28 and rectangular base with dimensions 4 and 7

27 Suppose that S and T are linear mappings with standard matrices 3 7 S 2 4 T T 1 402 2 1 3 a Determine the domain and codomain of S and T b Determine So T and TOS

Determine the standard matrix of a reflection in R2 in the line 3x 2x2 0 Enter an exact answer below b sin a 3 2 C E G

Compute the result of counterclockwise rotation of a vector x a sin a 8 a S 3 by an angle 2

You are given the 2 x 2 matrices 11 1 11 1 11 Solve the matrix equation below for X A X I 18 5 7 B 16 10 135 C 0 ATC X CA AC

You are given the 2 x 2 matrices 3 8 12 4 19 8 1 1 2 0 3 C 3 X A Solve the matrix equation below for X AX B 2 C

A pilot is flying over a straight highway He determines the angles of depression to two mileposts 4 8 mi apart to be 29 degrees and 43 degrees Find the distance of the plane from point A and find the elevation of the plane

Create a linear model for the data in the table X y 2 7 6 11 Write a linear model for the data in the table y 0x 0 9 14 10 16 11 18 13 21

9 points Question 1 Given that 1 u 2 v 2 C 17 d is a unit vector find c 3 4d is a unit vector find d

What is the exponent on x 3x Expand 3xxx 4xxxxx 12X then simplify What is the exponent on x Expand 3x2 then simplify What happened to the 3 What is the exponent on x 12x8 How could you determine the number of x s without expanding How could you determine the number of x s without expanding How could you determine the number of r s without TEV

5 The span of a given set of vectors is guaranteed to equal R if the span contains the following three vectors 9 00 Use this fact to check whether the following vectors span R 3

3 2 3 xy xy doesn t exist 13 Show that the lim x y 1 2 x y 8

Flag question Assuming the following distribution 1 4 5 7 9 120 which measure of location is best

a Find the eigen values and eigen vectors of the matrix A 8 6 2 6 7 4 2 4 3

Divide 6x5 7x4 8x 9x 10 2x 3x 1

whatever s right dude O c Yes that s reasonable Clear my choice You work full time 40 hours a week You years When you are fired you have 5 we employer pay you when you are fired for

Show that B is the inverse of A 1 2 2 1 1 1 9 9 12 A STEP 1 Find AB AB STEP 2 Find BA BA 1 3 3 6 0 3 6 1 0 9 1

Use synthetie division to find the 2x 2 8x 2 19x 30 is result when divided by r 6

ou should check the 3 axioms of a subspace Determine if U is a subspace of the indicated vector space U y 4 V R R Then find a basis for U

plane flies 520 kilometers with a bearing of 316 clockwise from north from Naples to Elgin The plane then flies 710 kilometers from Elgin to Canton see figure Canton is due west of Naples Find he bearing of the flight from Elgin to Canton Round to the nearest whole number O N W E S Canton Elgin Not drawn to scale b 44 Naples

Is this a How can we tell if it is or is not a function Type a response

Use the true conditional statement shown below State the conve If a number is divisible by 4 then it is divisible by 2 OA If a number is divisible by 2 then the number is not divis OB If a number is not divisible by 2 then the number is not OC If a number is divisible by 2 then the number is divisible

The Woodson s want to set aside 100 000 for each of their two children by the time each one starts college They have 6 years remaining for 1 child and 8 years for the other They started the college fund several years ago and the fund earns 7 per year and has a current balance of 75 000 How much do they need to contribute to the fund each year in total to meet their goals if they can increase their savings contributions by 3 every year Assume that the annual contributions occur at the end of the year For simplicity assume that they will withdraw the entire 100 000 for Child 1 at the end of year 6 and the entire 100 000 for Child 2 at the end of year 8 Hint Use Excel to find the starting contribution that achieves the goal and leaves the investment fund at zero after the 100 000

Solve the system of three linear equations by using the Matrix Method and the Inverse Matrix Method and determine if the system is consistent or inconsistent x 2y 3z 0 3x 2y z 0 3y z 0

The sum of the squares of the eigenvalues of the following matrix 4 OA 12 OB 36 OC 2 OD 3 OE 14

7 20 pts Use Gaussian Elimination to find the values of k if any such that the system below has a no solution b a unique solution and c infinitely many solutions Show elementary row operation steps This is an exam problem Help is NOT allowed x 2y 3z 1 2x 4y z 2 3x 6y kz 3

4 In the figure below ADEF ANPL Find the lengths of the missing sides E N T D 4 2 m 15 3 m 7 8 m P

3 If lines L and M are parallel find x y and z Explain your reasoning M y 43 Z

Let u 2 3 3 and A 6 8 16 12 2 23 5 01 Is u in the subset of R3 spanned by the columns of A Why or why not Select the correct choice below and fill in the answer box to complete your choice Type an integer or decimal for each matrix element O A No the reduced echelon form of the augmented matrix is which is an inconsistent system B Yes multiplying A by the vector writes u as a linear combination of the columns of A

If f and y are inverse functions and f 4 10 what is y 5

1 Solve the initial value problem Polutions x y dx 2xy x 1 dy 0 y 1 1

1 point Consider the linear code with check matrix Find a generator matrix for this code Answer G H 1 1 1 1 1 0 1 1 0 0 1 0 1 1 00 0 1 0 0 0 0 1 0 00 01

ramer s Rule has been used to solve for one of the variables in a system of equations Determine whether Cramer s Rule was used correctly to solve for the variable If not identify the mi System of Equations Solve for z z 1 x 4y 2x3y z x y 4z 6 1 z 1 4 1 2 3 6 1 1 1 1 4 1 2 3 1 1 1 4 O Cramer s Rule was used correctly to solve for z O Cramer s Rule was not used correctly to solve for z The given setup solves for x not z O Cramer s Rule was not used correctly to solve for z The given setup solves for y not z

13 Automobile X accidents can cause severe A Financial Loss X B Physical Harm C Emotional Problems D All of the above

24 Liability insurance only covers bodily injury to others and damage caused to the vehicles or property of others A True B False

17 An endorsement is a form added to an existing insurance contract that changes the terms coverage or scope of the policy A True B False

In a total respondents of 21 students about how many should be the number of classes when the data to be gathered is presented on FD

elect the Venn diagram that represents the set below U hoose the correct answer below A C I G F LL E C This question 1 point s possible B G D G F F U U

7 Consider the matrix 3 3 3 L4 4 0 a Write A as a product of elementary matrices with A included in the product write the actual elementary matrices b Write A as a product of elementary matrices with A 1 included in the product write the actual elementary matrices

A function is defined by f x 3 where x 0 Find f 1 x Select one a b O C d 4 HI x 1 x 1 X 1

Solve the three part inequa 3 2x 1 1 The solution set is Tiet in inter

5 7 3 3 4 2 4 d Evaluate the determinant of B by a cofactor expansion along the third column You can use t computations from part b Consider the matrix B

e answer above is NOT correct Determine the value of h such that the matrix is the augmented matrix of a consistent linear system 4h 12 6 5 15

4 Write the solution set for 30 3x2 2x3 0 that is find 31 11x2 6x3 0 all solutions to the system Show Transcribed Text

prove that f x 2x 1 for xER using the epsilon and delta definition

AA N 5 0 5 10 one 5 y 4 sin x y cos x 4 y cos x 4 y 4sin x 5 10