Matrices & Determinants Questions and Answers
Algebra
Matrices & DeterminantsDetermine if the matrix below is invertible Use as few calculations as possible Justify your answer 1 4 7 4 3 5 0 0 2 SCOOB Determine if the matrix below is invertible Use as few calculations as possible Justify your answer OA The matrix is not invertible In the given matrix the columns do not form a linearly independent set OB The matrix is not invertible If the given matrix is A the equation Ax b has no solution for at least one b in R OC The matrix is invertible The given matrix is not row equivalent to the nxn identity matrix OD The matrix is invertible The given matrix has 3 pivot positions
Algebra
Matrices & Determinants4 What elementary row operations applied to 3 1 1 27 2 30 1 12 will yield the following matrix 3 5 2 30 0 3 1 2
Algebra
Matrices & Determinants7 10 points Apply Cramer s rule to solve the following linear system 21 1 1 2 2x x 50 7 2r 0 Use any formula of choice to compute all the associated determinants Show all your work
Algebra
Matrices & DeterminantsTwo augmented matrices for two linear systems in the variables x y and z are given below The augmented matrices are in reduced row echelon form For each system choose the best description of its solution If applicable give the solution b 10 2 01 0 LO O O 10 1 012 000 8 0 The system has no solution O The system has a unique solution x y 2 0 O The system has infinitely many solutions x y z x x x D x y z 1 The system has no solution The system has a unique solution x D The system has infinitely many solutions x z x D C x 2 x x x 2 00 X
Algebra
Matrices & Determinantsthe matrix elect one 210 a 2 R R Ob 2 R R OC 2 R Od 2 R R 2 R R was obtained from by an elementary row operation Which of the following describes the elementary row operat
Algebra
Matrices & Determinants16 Let A X 9 1 1 y 4 270 If the kernel of A contains the vector what are x y and z 2 3
Algebra
Matrices & Determinantsof Which of the following is the reduced row echelon form for the augmented matrix of x 2yz 8 x 3y 2z 3 2xy 32 19 Select one a g this question for future reference 001 O b OC O d e 00 01 0 3 0 0 100 010 001 0 20 1 0 0 100 010 0 00 3
Algebra
Matrices & DeterminantsThe augmented matrix in echelon form of a system of linear equations in x and y is given below Find x and y 33 Enter the exact answers X i
Algebra
Matrices & DeterminantsIn the following exercises express the limits as integrals n 60 lim x Ax over 1 3 i 1 n 61 lim 5 x 3 x A over 0 2 3 n x i 1 n 62 limsin 2x Ax over 0 1 i 1 81x
Algebra
Matrices & DeterminantsFind the inverse of the function on the given domain X f x f x 2 812 18 00 RHD
Algebra
Matrices & DeterminantsExercise 3 6 7 Let a e3 a2 e and a3 e2 be the vectors of the ordered basis A for R a Find the transition matrix S for the change from the standard basis to A b use S to find the components of x 3 4 5 in the basis A and c find the representation MA of the matrix M 1 1 1 2 2 0 3 0 0 relative to the basis A
Algebra
Matrices & DeterminantsQuestion 6 entify the x intercept of the function y 4 The function has no x intercept 1 81 4 81
Algebra
Matrices & Determinantsformulas for the entries of M where n is a positive integer M 2 M 3 4 8
Algebra
Matrices & Determinantssider the following B 1 2 1 1 B 12 0 4 4 1 x g a Find the transition matrix from B to B b Find the transition matrix from 8 to B P c Verify that the two transition matrices are inverses of each other Pp 1 LI d Find the coordinate matrix x g given the coordinate matrix x
Algebra
Matrices & DeterminantsFind all steady state vectors for the given stochastic matrix A X 0 09 0 08 0 09 part b 0 08 0 Show Transcribed Text Fill in the missing values to make the following matrix a stochastic matrix 0 35 0 54 0 06 0 27
Algebra
Matrices & Determinants2 A 50 meter vertical tower is braced with a cable secured at the top of the tower and tied 30 meters from the base What angle does the cable form with the vertical tower
Algebra
Matrices & DeterminantsQuestion 24 3 3 points Using a Standard Normal Distribution what z score has an area of 892 0 108 0 814 A
Algebra
Matrices & DeterminantsFind the points on the graph of the polar equation where the tangent line is horizontal or vertical Assume 0 0 2 Enter your answers as a comma separated list of ordered pail r 1 cos 0 horizontal tangent smallest 8 value argest 8 value wertical tangent smallest 8 value argest 8 value r 0 r 0 r 0 r 0 r 0 r 0 117
Algebra
Matrices & Determinants6 Find the least squares solution to ther overdetermined system Ax b Also find the orthogonal projection of b into Col A A 1 1 1 1 3 1 b 3 0 8
Algebra
Matrices & Determinantsfind the standard matrix for the reflection T of R 3 in the line x 2t y t z 2t Is T invertible
Algebra
Matrices & DeterminantsUse the factorization A PDP 1 to compute A where k represents an arbitrary integer 19 a 0 1 9 01 0 b 0 1 a 9 b a O
Algebra
Matrices & DeterminantsDiagonalize the following matrix 400 140 005 Type an integer or simplified fraction for each matrix element OC The matrix cannot be diagonalized
Algebra
Matrices & Determinants1 point Find a basis of the subspace of R4 that consists of all vectors perpendicular to both Basis 1 0 7 5 and 0 1 6 5
Algebra
Matrices & DeterminantsFind a power series for the function centered at c 1 9 x f x 8 n 0 f x I C 2 Determine the interval of convergence Enter your answer using interval notation
Algebra
Matrices & Determinants11 Only one of the following matrices has an inverse Find the determinant of each matrix and use the determinants to identify the one that has an inverse Then find the inverse 1 4 1 0 1 0 1 A 0 2 B 14 0 0 20 301
Algebra
Matrices & DeterminantsLet S 1 2 3 and f1 f2 f3 Fun S be given by Find a nontrivial linear relation among these vectors f f f3 0 fi 1 2 fi 2 0 f2 1 2 f2 2 6 f3 1 3 f3 2 9 f3 3 9 f 3 5 f2 3 4
Algebra
Matrices & Determinants60 Question 4 14 2 points In the following data set what word would best describe the data entry 10 10 18 18 19 19 20 21 21 23 23 24 27 Bias O Outlier O Range O Mean Question 5 14 3 points Consider the following histogram in which a student created a histogram about the heights of males in his classroom 5
Algebra
Matrices & Determinantstra Credit Add or Subtract Write your answer in standard form 1 4 coefficient and degree 1 2x 3x 9x 2x 8x 11 s completely 2 16p 4 4 4x 8x 4x 20 HW 12 Subtract from
Algebra
Matrices & DeterminantsThe below permutation matrix P changes the second and third rows of matrix A when A is multiplied with P PA Find the unknown values in P P f 1 d e h b 1 a C 2 i O a b c def g h i 1 0 2 4 g 0 47 1 46 44 4 O
Algebra
Matrices & DeterminantsLet T R R be a linear transformation such that T 1 1 1 3 0 1 T 0 1 2 3 4 1 and T 1 0 1 0 1 1 Find the indicated image T 2 1 1 T 2 1 1
Algebra
Matrices & DeterminantsFind a singular value decomposition for each of the following matrices 9 a 2 b 0 1 0 0 02
Algebra
Matrices & DeterminantsAfter a person takes a pill the drug contained in the pill is assimilated into the bloodstream The rate of assimilation minutes after taking the pill is R t te 0 4t Find the total amount of the drug that is assimilated into the bloodstream during the first 15 minutes after the pill is taken Round your answer to 2 decimal places 0 23 6 25 0 38 6 14
Algebra
Matrices & DeterminantsA 6 1 5 3 2 8 2 1 7 4 6 7 7 6 55 10 6 3 6 Enter the singular values of A in decreasing order into the answer box below separated with com
Algebra
Matrices & Determinants4 Solve each triangle Round your answers to the nearest tenth of a unit a b T 5 cm 7 cm R 9m S U 10 m c In AHIJ LI 90 i 1 5 m and ZJ 21 P d In ABCD LC 90 b 12 0 cm and d 13 5 cm e In ALMN LM 90 1 9 6 m and LN 34 2
Algebra
Matrices & DeterminantsA P 1 1 where Pis the initial amount The equation for compound interest is A P invested r is the interest rate as a decimal n is the number of times compounded annually and t is the number of years A person is investing 1000 at an interest rate of 12 interest for 25 years and is curious how much difference the number of compounds n increases the value of the account after 25 years She created the function A n 1000 100 1 0 12 25 What would best describe an appropriate domain of the function The set of Integers i e 2 1 0 1 2 The set of Natural Numbers i e 1 2 3 4 The set of All Real Numbers R where 20 A
Algebra
Matrices & DeterminantsConsider the function f x W Oy 0 None 4x find any horizontal asymptotes if they exist 3x 2
Algebra
Matrices & Determinants3 12 12 3 6 6 6 with rational entries and a diagonal matrix D such that D PT AP Let A P 100 100 6 6 Find an orthogonal matrix F D
Algebra
Matrices & DeterminantsDetermine the type and stability of each real equilibrium point by calculating the Jacobian matrix at each equilibrium a b c x 1 xy y x y x x 3y 2xy y 4x 6y xy x 4x x xy y 4y x y y
Algebra
Matrices & DeterminantsLet 1 A 3 5 Find bases for Row A Col A and Null A 2 1 5 3 6 1 15 2 10 1 25 4
Algebra
Matrices & DeterminantsGraph the functions 10 y 3 2x 6 5 4 3 2 1 0 1 2 3 4 5 6 x TIG 7 1 a at w No to L T 7 11 f x 4 x 1 MEE 6 5 4 B 1 I YA 2x O 1 2 3 4 5 6 x 23 CHIL CHIL nit F 12 g x 2 E 6 5 4 3 LLL J 1 56 ol 1 2 3 4 10 5 6 x
Algebra
Matrices & Determinants4 6 y 2 and u 3 3 Compute the distance from y to the line through u and the ori
Algebra
Matrices & DeterminantsScalene Triangle A MATH MONKS B C If the Measure of ZA 94 and the measure of ZB 91 what is the measure of ZC
Algebra
Matrices & Determinantser 5 6 Mastery Quiz Determine whether the given ordered pair is a solution of the system 1 4 3x 2y 5 2x 5y 29 O solution Question 10 o not a solution