Matrices & Determinants Questions and Answers

20 points Find the orthogonal projection of onto the subspace W of R spanned by and 8 23

1 point Find the eigenvalues 2 3 and associated unit eigenvectors 2 3 of the symmetric matrix 6 2 2 2 The eigenvalue 8 has associated unit eigenvector The eigenvalue 12 0 has associated unit eigenvector he eigenvalue 13 6 has associated unit eigenvector 3 A 1 1 8 T 0 2 2 2 6 2 2 1 6 1 6 2 2 2

Find the inverse of the linear transformation T R R defined by 7 x y x y 2x y Verify that T 7 3 2 3 2

A baseball diamond is a square 94 0 ft on a side with home plate and the three bases as vertices The pitcher s position is 61 5 ft from home plate Find the distance from the pitcher s position to each of the bases 3rd base 2nd base 61 5 ft Home plate The distance from the pitcher s position to 1st base 2nd base and 3rd base is Round to the nearest tenth as needed 94 0 ft 1st base ft ft and ft respective

DE in the span of the vectors Is the vector 34 5 34 If SO find and enter the necessary coefficients If not enter DNE in both boxes 2 6 1 6

1 Find the best straight line fit to the given data points 1 3 2 4 and 7 0

4 Consider the vectors v H V2 H V3 2 a Verify that the vectors are linearly independent b Find an orthonormal basis for span 1 U2 U3 10 points

Given the triangle below choose the order s you should find the angles using the Law of Cosines to find the first angle followed by the Law of Sines to find the second angle Picture is not drawn to scale There may be more than 1 correct answer 27 A 18 36 B CD

8 8 6 4 2 4 N 2 4 6 8 4 4 2 0 2 4 2 4 6 8 X

Provide the missing information If no horizontal line intersects the graph of a function fin more than one point then fis a function

x 4y 2z 3x 2y 3z 2x y 3z 0 4 1

5 2x 2y 3 2x 2y 3 7 3x y 6 3x y 2 Solution 6 2x y 10 5x y 12 35 by 12 zy 8 3x X 9 14 43 Check Solution Check

5 4x 3y 14 y 2x 2 x 5 12 ETA 2 4 7 x 3y 18 2x y 1 Check Solution Check 6 y 3x 9 5x 8y 14 8 y x 2 3x 6 Y X 2 3x b Check Solution Check

a Find an eigenvector of the matrix 2 17 3 19 11 11 2 2 2 3 2 11

Bank 02 04 C1 The graph below represents the money collected at the skating rink on Friday Find the domain when the maximum number of people allowed in the skating rink is 75 people Amount of Money 600 400 200 50 O0sy 75 20 y 320 0 x 75 20 x 320 Number of People 100 150 wired question

2 Find the discriminant of the equation and give the number a the equation x 6x 16 0 U Font Family V AA A

ABCDE JKLMN What is the value of q and r in the diagram below Set up proportions to solve The Vowe Of 15 175 20 E B 9 D 8 N 7 M L 20 100

Find the eigenvalues and eigenfunctions of the given boundary value problem Verify orthogonality of the eigenfunctions Start by writing the ODE in the Sturm Liouville form y 8y 16 y 0 y 0 0 y 0

At 3PM Roger Dodger drives onto the Highway 880 Ramp at Milpitas going Northward in a 65 mph zone A police officer clocks his speed at 60 mph Four miles away at 3 03 PM Roger Dodger see another police officer clocking him going 57 mph Can the police officer legally write Roger Dodger a speeding ticket How do you know this

Compute det B where B 1 2 1 0 1 3 3 1

Consider the linear system in matrix form AT b where 2 3 1 A b 3 4 1 9 The sum of the elements in the solution vector x A 12 B 16 11 C 4 D 16 2012 1 X2 i e x x is given by

Find the annual percentage yield for an investment that earns 6 per year compounded monthly Round your answer to two decimal places

Perform the matrix operation If not possible enter IMPOSSIBLE in any cell of the matrix 1 1 3113 1 5 3 5 5 5 5 4 1 1

Jason Ayers works as a lifeguard earning 8 75 an hour for 20 hours per week What is Jason s straight time pay for the week O 170 50 O 175 00 O 170 00

and 25 per hour for snow remo still in school he is only allowed to work for at most 20 hours per week His goal is to make at least 300 per week Create a syste WIC SITUA Graph the HT mes that erine the variables you use qualition dentify a solut To the systons

Use the average daily balance method to compute the amount of interest that will be charged at the end of the billing cycle Use a 365 day year Month May 31 days Previous month s balance 960 Interest rate 18 Date Transaction May 3 made payment of 380 May 12 purchase of 105 May 21 purchase of 95 May 29 made payment of 65 A 10 70 B 7 45 C 8 28 OR 11 66 EXTE

2 5 points For what values of a and b will infinitely many solutions 2 1 2 a SR 1 have no on

Simplify x 3 x 3 x 4 x 4 x 4 x 5 3 x 3

11 Find the transition matrix from B 2 4 1 8 1 20 A 14 2 4 4 1 C 14 2 1 2 2 0 4 B 14 2 4 1 14 8 2 0 2 D 14 17 9 0 8 8 8 to B 4 0 6 1 2 2 1 2 2 2 Q 2

5 18 Find an invertible matrix P such that P AP is diagonal where A 5 B P 1 5 A P 5 1 C P 80 06 D P 06

43 Divide and simplify x x 12 2x 8 2x 5x 3 8x 4

Let x y z be non zero vectors and suppose w 2z If z 2x 2y then w 4x 4 y Using the calculation above mark the statements below that must be true A Span w x Span w z B Span x y Span y z C Span w x z Span x y z D Span w y z Span w x E Span w z Span x z

Plot 76 and 1 11 14 on the number line below

and B then verify that A If a 1 2 3 5 7 9 2 1 1 4 1 5 1 2 0 1 3 1 B 1 A 1 B 1 and A B 1 A 1 B 1

The sum of twice a number and six is 32 Find the number

Find if possible the inverse of each of the following matrices 5 2 1 6 3 1 6 a 6 5 9 9 4 3 0 b 1 1 2 4 01

By using the Cayley Hamilton Theorem find e At of the following matrix A 1 2 2 3

What are the values of x and y in the matrix subtraction below 20 4 9 16 0 6 X 15 O y 15 O X 15 y 17 O x 25 y 15 5 6 1 X 7 10 11 9 y 7 17

What was the major weakness of the Continental Drift Theory formulated by Alfred Wegner was OE It could not estimate the speed of plate motion per year O The theory relied on plants and animal fossil records to show that all continents were one unit before they broke apart The theory could not explain why the plates moved apart It is outdated and has no relevance for the study of present day geological processes O The theory was formulated by a non geologist who was not a scientist

1x log 1 2 x 6 Then give the domain and range 17 Use the graphing tool to graph the function Click to enlarge graph The domain is Type your answer in interval notation The range is Type your answer in interval notation

A gas is contained in a thick walled balloon When the pressure changes from 417 mm Hg to 576 mm Hg the volume changes from L to 4 78 L and the temperature changes from 497 K to 386 K

4 5 marks Solve for X where A B X 19 and B 1

Listen Which of the following expressions is equivalent to cos 0 1 sin 0 a 1 cos 0 Ob 1 tan 0 O c 1 sin 0 d 1 sin 0 Question 40 1 point Listen Which of the following is not equivalent to tan x

Listen Find all of the solutions of 2 sin x 3 sin x 2 0 between and O a x and 5 Ob x and 5 c r and 5 Od r and 5 Question 19 1 point 4 Listen

Question 10 1 point Listen Convert 315 to radians O a IT O b St Oc 3 Od 1 Previous Page Next Page

Convert 15 to radians O a 1 2 Ob 6 c 3 O d

Find the projection of this matrix onto the xy plane 5 1 0 3 2 1 0 0

Show that the vectors y that satisfy the equation 2 form a subspace of R of dimension 2 2x 3y 5z 0

ind the standard form of the equation of the hyperbola with the given characteristics Vertices 5 3 5 7 Asymptotes y x 10 y x

632 7 1 Let C 3 2 6 and D 6 2 5 5 640 Find DC if it is defined Otherwise click on Undefined