Matrices & Determinants Questions and Answers

Write the English phrase as an algebraic expression Let x represent the number Eight less than a number The phrase written as an algebraic expression is N
Algebra
Matrices & Determinants
Write the English phrase as an algebraic expression Let x represent the number Eight less than a number The phrase written as an algebraic expression is N
The slope m and a point P on a line are given Use the information to find three additional points on the line m P 5 6 3 Determine three points on the line with slope O A 2 8 2 11 6 14 O B 8 2 11 2 14 6 O C 9 1 12 3 15 7 On 1 0 2 121 1 7 151 and passing through 5 6
Algebra
Matrices & Determinants
The slope m and a point P on a line are given Use the information to find three additional points on the line m P 5 6 3 Determine three points on the line with slope O A 2 8 2 11 6 14 O B 8 2 11 2 14 6 O C 9 1 12 3 15 7 On 1 0 2 121 1 7 151 and passing through 5 6
1 Solve each equation 1 x 6 10 A 4 16 C 4 B 8 26 D 20 0
Algebra
Matrices & Determinants
1 Solve each equation 1 x 6 10 A 4 16 C 4 B 8 26 D 20 0
Find an equation of the line L 10 8 61 40 Q
Algebra
Matrices & Determinants
Find an equation of the line L 10 8 61 40 Q
Simplify the following expression 4 C C
Algebra
Matrices & Determinants
Simplify the following expression 4 C C
2 1522 customers at a major retailer were surveyed whether or not they made a purchase and were satisfied with the service they received The table below organizes the responses Satisfied with Service Not Satisfied with Service Total Made a Purchase Did Not Make a Purchase Total Answer 1 pt 130 715 845 Reasoning Explanation 1 pt 494 183 677 a 2 ts What is the probability that a shopper selected at random made a purchase given that they were not satisfied with the service Write your answer as a fraction 624 898 1522 b 1 pt What is the probability that a shopper selected at random made a purchase or was satisfied with the service they received Write your answer as a fraction
Algebra
Matrices & Determinants
2 1522 customers at a major retailer were surveyed whether or not they made a purchase and were satisfied with the service they received The table below organizes the responses Satisfied with Service Not Satisfied with Service Total Made a Purchase Did Not Make a Purchase Total Answer 1 pt 130 715 845 Reasoning Explanation 1 pt 494 183 677 a 2 ts What is the probability that a shopper selected at random made a purchase given that they were not satisfied with the service Write your answer as a fraction 624 898 1522 b 1 pt What is the probability that a shopper selected at random made a purchase or was satisfied with the service they received Write your answer as a fraction
Find the midpoint of the segment with the given endpoints 6 10 and 6 5 The mic Type a each ca
Algebra
Matrices & Determinants
Find the midpoint of the segment with the given endpoints 6 10 and 6 5 The mic Type a each ca
Intial Month Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Month 11 Month 12 24 Annually 1 500 00 1860 Balance 6 Quarterly 1 500 00 1590 16 85 4 2 Monthly 1 500 00 1786 551 1843 7 1530 1560 6 1591 8 1623 6 1656 1 P
Algebra
Matrices & Determinants
Intial Month Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Month 11 Month 12 24 Annually 1 500 00 1860 Balance 6 Quarterly 1 500 00 1590 16 85 4 2 Monthly 1 500 00 1786 551 1843 7 1530 1560 6 1591 8 1623 6 1656 1 P
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
Multiply 8k 5 9k 1 8k 5 9k 1 Simplify your an
Multiply the monomials 4x y6 8x y
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
Multiply the monomials 6a 9a6 6a 9a6
Simplify using the product rule y y6
Algebra
Matrices & Determinants
Simplify using the product rule y y6
Simplify the expression p p p 3 3 p p p Simplify your answer
Algebra
Matrices & Determinants
Simplify the expression p p p 3 3 p p p Simplify your answer
Rationalize the denominator 11 N
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
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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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
Combine like terms in the following expression 5a 3b 8a 4b 4 5a 3b 8a 4b 4 Simplify your answer
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Compute the dot product u v 6 15 U 5 15 O 195 30 255 225 V
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
Matrices & Determinants
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
Algebra
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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
Algebra
Matrices & Determinants
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
Algebra
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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
Algebra
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10 Factor the expression a 12a b 18a6b 30a b
Solve m x x 5x 6
Algebra
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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
Algebra
Matrices & Determinants
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