Matrices & Determinants Questions and Answers

a Solve the following system of linear equation using Gauss elimination method Y 2z 2 I X 2y 2x ay 2 52 2 b b Find the condition on a and b such that the system has infinitely many solution c If b 4 Is the system of linear equation non homogeneous Give a reason

Find the product 4x 4 4x 4 16x 16 4x 4 4x 4 16x 16 Simplify your ans

Multiply 8k 5 9k 1 8k 5 9k 1 Simplify your an

Multiply the monomials 4x y6 8x y

Simplify the expression 3p q4 6 6 3p q4 Simplify your answer Use integers or fractions for any numbers in the or

Multiply the monomials 6a 9a6 6a 9a6

Simplify using the product rule y y6

Simplify the expression p p p 3 3 p p p Simplify your answer

Rationalize the denominator 11 N

3 Let A 6 1 3 1 and u 3 C 5 15 B3 c 23 a Compute Au and Ac if possible If not possible explain why not b Does the matrix equation Ar c have a solution c Does the matrix equation Ar b have a solution for any choice of b R d Restate the above question as a computationally equivalent question as done in page 2 of the notes

What is the equation of the graph that represents the parent function f x x stretched vertically by a factor of 2 and then shifted up 3 spaces A g x 2 x 3 OB g x 2x 3 C g x 2x 3 OD g x 2 x 3 4

Use the unit fractions 36 in 1 yd Convert 6 yd to cm and 2 54 cm 1 in 6 yd is cm Type an integer or decimal rounded to the nearest hundredth as needed

The following system has an infinite number of solutions Form an augmented matrix then write the matrix in the reduced form Write the reduced form of the matrix below and then write the solution in terms of z The required augmented matrix is where 11 1 a21 0 a315 and x 0 7 a12 2 1 4 a22 a32 2 3 3 a13 2 1 a23 1 a33 1x 2x 3x 3 2y 2z 4 4y 12 2 2y 3z 6 a11 a21 a31 1 1 a12 a13 b b2 a22 a23 a32 a33 b3 b b b3 4 1 2 6 y 2

For the following matrix A 1 1 1 1 1 1 1 1 1 a Find the eigenvalues Explain how you can determine one eigen value A without any calculations b For each eigenvalue find the corresponding eigenvector s c Starting with the eigenvectors you found in b construct a set of orthonormal vectors using the Gram Schmidt procedure

eneral Form f x a x h k h is negative the graph shifts h units to the h is positive the graph shifts h units to the k is positive the graph shifts h units to the k is negative the graph shifts h units to the a there is a vertical stretch there is a vertical compression negative in front of the grouping symbol reflects the graph across the a

POLITICS The approval rating R t measured as a percent of a clas officer during her 9 month term starting in September is described by the graph where t is her time in office Percentage 8 8 8 8 40 20 2 Check 4 Months During which month is the approval rating increasing 6 8 October Choose December Choose April Select one Choose The graph below represents y x 41 2 2 O

In a volcano erupting lava flows continuously through a tube system about 16 kilometers to the sea Assume a lava flow speed of 0 5 kilometer per hour and calculate how long it takes to reach the sea It takes hours to reach the sea Type an integer or a decimal CE

Which inequality is represented by the graph y x 3 0y r 3 Oy x 3 Oy x 3 y 5 4 3 2 1 5 4 3 2 1 2 3 2 3 4 5

Simplify 5y 5y 2y 3 3y 9y 10 5y 5y 2y 3 3y 9y 10 Do not facto

Add the polynomials Express the answer in standard form 5p 3p 5 3 3p 3p 5p 3p 5 3 3p 3p Type your answer in standard form

Add the polynomials 5x 5 4x 4 5x 5 4x 4 Simplify your answer Type your answer in standard

Solve 006 5xt2 6 3 x 30 3 70h 2 11 Find the error 9x 18 3x 1 9x 18 2 9x 20 x 20 22 5 3 16 and correct it identify the terms and the coefficients of the expression 0 20 5p 7z identify the factors of the terms of expression The number of bees that visit a plant is 500 times the of plant is alive where represents the of years the plant is alive What does the expression 500 represents years the the price of a sandwich is 150 more than the price of a smoothie which is d dollars What does expression dit 105 represent curite an algebraic expresion to model the given content Give your answer in simple form 20 The price of a pair of shees plus 5 Sale tar

From the table below find f 0 and f 30 Find two values of x for which f x 15 Explain why f x is a function x f x Enter the answers for x in increasing order f 0 30 f x 15 when x THE 0 30 15 15 30 0 45 15 60 30 and x THE

Simplify the following expression by combining like terms 4 z 5 8z 4 z 5 8z

Rewrite the following without an exponent 0 2 3 2 8 08

Evaluate the expression when a 8 b 9 and c 2 b 4ac 6 4ac 2 when a 8 b 9 and c 2 Simplify your answer

Combine like terms in the following expression 5a 3b 8a 4b 4 5a 3b 8a 4b 4 Simplify your answer

Americans trust in government and the media has generally been on a downward trend since pollsters first asked questions on these topics in the second half of the twentieth century Trust in government hit an all time low of 14 in 2014 while trust in the media bottomed out at 32 in 2016 The bar graph shows the percentage of Americans trusting in the government and the media for five selected years Use this information to answer parts a c a Use the information in the graph to estimate the yearly loss in the percentage of people trusting in government The yearly loss in the percentage of people trusting in government is Round to the nearest tenth as needed Percentage 70 60 50 40 30 20 10 Trust in media Trust in Goverment 55 36 32 47 2003 2007 44 20 19 39 Save 41 17 2011 2015 2019 C C

Find a basis for the subspace spanned by the given vectors What is the dimension of the subspace 5 7 16 2 18 3 5 3 6 3 A basis for the subspace is given by Use a comma to separate vectors as needed

Determine the place value of the digit 3 in the whole number 3587 Choose the correct answer below O tens O hundreds Othousands O ones

Solve each inequality graph the solution on the number line and write the solution in interval notation 7 1 84 a Solve the inequality 13 3 39 y 24 24 Inequality notation solution O Contradiction no solution O Identity all real numbers b Graph the solution on the number line NOTE If there is no solution place an Open Dot at the center of the graph 3 2 Clear All Draw c Write in interval notation 0 Interval notation solution No colution 2 3

Compute the dot product u v 6 15 U 5 15 O 195 30 255 225 V

Hello Evaluate the determinant 60 0 1 5 7 5 3 6 The value of the determinant is

Triangle ABC is translated using matrix subtraction Which represents the resulting vertices after the translation

10 1 point The solution to the system of equations is 1 7 5x y 12 4x y 3 True False

8 1 point Solve the system of equations by substitution 7x 2y 13 x 2y 11 O 3 4 infinite solutions 2 5 3 4

Write the equation of the ellipse that has a center at 5 1 a vertex at 5 8 and a covertex at 1 1

Solve the following inequality and graph your solution 2x 8 24 4x X ame 6x 2417x Possible solution Wednesday Thursday Homework 16 mplify the expressions 2 x 3 4 x 5 x 3 5 What value of x makes the equation true 4 3 2 x 3 x 6 8 What is the solution to x 5 2 x 3 x 23 3 Friday Homework Name Solve the following equations for y 3x 7y 1 2 6 y 3 1 2x

a State and prove the Cayley Hamilton The b Let T be a linear operator defined on a vector space V F for n Zt Let A be a matrix representation for T with respect to some basis for V i Prove that the minimum polynomial of a linear operator T is well defined Hint Prove existence and uniqueness 7 marks ii Shout that is an oigonumlue of the linear operator A if and only if

5 09 HC A message in a bottle is floating on top of the ocean in a periodic manner The time between periods of maximum heights is 26 seconds and the average height of the bottle is 12 feet The bottle moves in a manner such that the distance from the highest and lowest point is 6 feet A cosine function can model the movement of the message in a bottle in relation to the height Part A Determine the amplitude and period of the function that could model the height of the message in a bottle as a function of time t 5 points Part B Assuming that at t 0 the message in a bottle is at its average height and moves upwards after what is the equation of the function that could represent the situation 5 points Part C Based on the graph of the function after how many seconds will it reach its lowest height 5 points LL Font Family AAT A E

3 05 01 5 05 5 07 MC Let 8 8 7 3 Part A What is a coterminal angle of 8 such that 0 0 2n 5 points Part B What are the exact values of all six trigonometric functions evaluated at 6 10 points

10 Factor the expression a 12a b 18a6b 30a b

Solve m x x 5x 6

Let L PR by L P p plos p 1 Compute the representation matrix for L the bases 1 x x x x x 23 on bor L w r t Pri 4

2 Factor completely Then identify the roots for the quadratic function below y 2x 10x 12

1 Factor completely 3x y z 9x yz

1 point The fifth term of the sequence will be 11 1 2 5 8 True False

7 1 point Write the first four terms of a sequence given the recursive rule below f n f n 1 4 for all n 2 and f 1 32 O not enough information 32 28 24 20 32 31 30 29 O 32 27 22 17 Previous

Skew lines are a pair of lines that are non intersecting non parallel and non coplanar This implies that skew lines can never intersect and are not parallel to each other Given two lines a b c 7 40 0 0 0 0 0 L y 3 t 1 and L y 6 t 0 1 Prove that L and L are skew lines Find a vector that connects these two lines 2 6 marks 3 marks Plane lies exactly halfway between the two lines and intersects neither Use the results in Question 4 b to find the Cartesian and vector equation of plane B 16 marks

5 1 point A rectangle has perimeter P length I and width w Which of the following represents I in terms of P and w 1 P w 1 2P 2w P 2w 1 2 1 P 2w Previous