Matrices & Determinants Questions and Answers

12 marks a 6 marks Given the matrices A and the reduced echelon form of A below find i a basis for Row A What is the dimension of Row A ii a basis for Col A What is the dimension of Col A iii a basis for Nul A What is the dimension of Nul A A 1 23 4 5 10 1 2 1 2246 4 1 1 20 1 b 2 marks Consider vectors rref A 1 0 1 0 5 3 1 1 0 8 3 0 0 0 0 1 1 3 0 000 0 V 1 1 5 2 V2 2 3 1 0 V3 9 10 34 14 V4 0 4 2 3 v5 3 31 41 87 in R4 Find a basis and the dimension of the subspace W span V V2 V3 V4 V5 1 0 7 05 01 1 0 4 00 016 00 000 NOTE RREF of the matrix whose columns are vectors V V2 V3 V4 V5 is c 4 marks Let A be an m x n matrix Prove that every vector in the null space of A is orthogonal to every vector in the row space of A

5 points Find all the values of k for which the matrix is not diagonalizable over C 0 1 0 0 1 0 0 k 8 k 9 Enter your answers as a comma separated list

Find the axis of symmetry and vertex from the graph below X Vertex 3 y 2 0 X

The matrix 43 48 113 122 73 116 126 112 192 209 131 213 171 116 31 1 66 97 was encoded using the matrix A 1 4 0 3 6 1 2 2 5 What is the message

Then where at 031 a12 033 0 To 10 619 A 8 7 2 in po sto to 150 D D D 40 923

Given that A is transformed into U by the elementary row operations below find L A L 3 6 2 9 16 11 9 18 12 Ex 42 C 3R Rs Rs 3 6 2 9 16 11 LO 0 6 3R R R 3 0 2 0 6 2 5 0 6

X Check Score ac X 1 2x 2 x 2 6 x 2 3 a Write the partial fraction decomposition of the improper rational expression 2x4 8x 7x2 8x 12 x 4x 4x 6 Hide Answer Try Another

1 Indicate the metric the length of a Choose the correc mm

Find the inverse of the following matrix using the Gauss Jordan method 6 173 253 108 75 80552 202

Consider the two matrices 200 2145 1 reflects about the line y 2z projects onto the line y a The matrix that reflects about the line y 2z and then projects onto the line y b The matrix that projects onto the lin

Write the division problem shown by each number li a 15 units 3 units 3 units 3 units 3 un b 1111 0 15 5 3 5 15 3 35 15 15 3 5 315 5 3 R4 8 units 71111111 0 4 8 368 AR4 6 9 36 units 8 units 8 u 12 16 20

gasoline station recently increased the price of one grade of gasoline by 5 If this gasoline originally cost 2 60 per gallon find the mark up and the new price

Question 15 Determine the zeros if any of the r O x 5 x 5 x 2

Question 14 Find the domain of f x x 2 x 4 all real numbers except x 2 and x 2 O all real numbers except x 2

Question 9 Determine the equations of any h f x 2x 5x 1 x x 1 O horizontal y 2 vertical x 1

Question 4 The graph of the function 3 x 2 is shown below Determine the vertical and horizontal asymp 10 8 6 4 10P H 864 H 2 J 22 NY 4 6 8 10 2 4 Take 6 8 10

Question 10 Determine the domain of the function f x O Domain all real numbers except x 1 Domain all real numbers ocent Y A and

3 Algebraically solve the following equations a cos 20 cos0 0 270 0 180 2 marks Hint There are 3 exact solutions for the given interval

Anti Semitism is discrimination against Jews Christians Germans 7

Match each system on the left with the number of solutions that it has on the right Answer options on the right may be used more than once x y 3 2x 2y 6 5x 2y 7 10x 4y 14 y 2x 1 4x2y 2 9x 6y 15 2y 1 3x no solutio one solutio infinite numbe of solutio

1 This DE is exact Try to find the solution to the IVP 3 sin x 3x cos x 4y sin x dx 4 cos x dy 0 y t 2

Antonio s friend Jessica was also on The Screamer when it broke Her seat was 65 feet above the ground What was her seat s angle of rotation Is there more than one possibility

4 x 2 x 3 5 4b 3 b 7 6 3k 1 3k 1

x y 2z 122 X y z 2x X Y 2 x 2y

DIRECTIONS Solve the equation 1 x 5 x 3 0 4 3n 11 n 1 0 2 2 13 z 14 0 3 d 7 d 0 5 2y 5 7y 5 0

What is the period of the graph Write your answer as a fraction in simplest form a b 40 The period is 11 3 11

Solve the system using substitut 2x 2y 6 7x y 27 No solution O Infinite number of solutions

The measure 89 of an angle is standard positi 1 2 radians

The measure 0 of an angle in standard position is given Find the exact values of cos 0 and sin 0 for 4x 3 radians 4x radians 3 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression COS 4x sin radians Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

The angle 750 rotates full times around the or

2 The number of people that smoke cigarettes in Bentley County has been decreasing at a rate of 7 per year At the beginning of 2020 the number of people who smoke in the county was 5000 Answer the following questions assuming this rate of decrease will continue a Write an exponential equation in the form y ab to model this situation b Fill in the table of values that models this situation c According to the model how many smokers will there be in Bentley County in the year 2030 Show your work X 0 1 2 m 6 Y

solve the problem est estimate of 60 4 Lisa s camera has 2 048 megabytes of memory for storing pictures She has already Buses 16 megabytes of memory How many Chigh quality pictures can Lisa store with the Sremaining memory Show your work 960 Answer

Consider the functions f x 6x 4 and g x x 4 a Find f g x b Find g f x c Determine whether the functions f and g are inverses of each other a What is f g x f g x Simplify your answer Give any values of x that need to be excluded from f g x Select the correct choice below and fill in any answer boxes within your OA x Use a comma to separate answers as needed OB No values should be excluded from the domain 4 b What is affix

Calculate the determinant D D a b cd a b d C Simplify your answer

w 6 w 7 Answer dV V D 88 Find the product 3 4d 2d 5 TT a

p 4p p 3p 15 Answer 1 0 d Find the sum Vo vo 0 0 TI 52

49 PELLARD FRANCHETTE Two large telecommunications companies are considering a merger The net income in billions of dollars of the first company can be modeled by the function A t 9 01t2 20 60t 23 55 where t is the number of years since 2013 The second company s net income also in billions of dollars can be modeled by the function B t 9 47t 21 46t 18 72 where t is the number of years since 2013 The function C t can be used to model the two companies combined net income in billions of dollars where t is the number of years since 2013 Write the function C t C 1 2 3

7 5 In each of the following triangles find the length of the side labeled x b 28 feet 47 meters 38 150 cm 32

has purchased a house that 4 A group of gives them a direct view of home plate although their view of the rest of the field is largely impeded by the outfield wall The house is 30 meters tall and their angle of vision from the top of the building to home plate has a tangent of What is the horizontal distance in meters from home plate to the closest wall of the fans house 7 6 home plate F 35 0 G 32 0 H 25 7 J 5 0 K 4 3 angle of vision 30 m

Lindsey Plochinsky Find Average Rate of Change from Equation Mar 07 10 01 33 AM Watch help video Given the function h x x 6x 17 determine the average rate of of the function over the interval 7 x 2

Show that the function f x y 2xy is differentiable at the point 1 2

1 point Let P be the vector space of all polynomials of degree 2 or less and let H be the subspace spanned by 5 5x4 x 2x and x 1 a The dimension of the subspace H is b Is x 5x4 x 2x x 1 a basis for P choose can explain and justify your answer c A basis for the subspace H is polynomial or a comma separated list of polynomials Be sure you Enter a

What is the degree of the polynomial that was graphed

Listen Determine an approximation for the instantaneous rate of change at x 2 for the function y 2 2 4 2K

Show all steps to prove the following 1T 2A sin 2x 2 cos x sinz tanz 1 cost

Question 10 Use synthetic division to divide 3x 10x 23x 10 x 5 O 3x 5x 2 O 3x 3x 10 O 3x 13x 6

Ve assume that in a village there are farmers carpenters and tailors who provide the three essential goods food housing and clothing Suppose the farmers consume of the food produced by farmers of the housing produced by carpenters and of the clothes produced by tailors The carpenter consumes of the food of the housing and of the clot The tailors consume of the food of the housing and no clothes Assume this is a closed Leontief model If we know that the tailors produce 72 units of clothes then the farmers produce units of food and the carpenters produce units of housing

21 AB is a radius of circle A CD is tangent to circle A at point B The equation of CD 3x 2 What i 4 312 dd d 2 Nic x 2 What is the slope of AB 7 G

10 When drawn in standard position an angle a has a terminal ray that lies in the second quadrant and who 9 sine is equal to Find the cosine of a in rational form as a fraction 41

Math gebra 1 M 7 Properties of matrices R 4 If F 8 6 6 1 5