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Linear Algebra
October 2022
Linear Algebra questions and answers in October 2022
. Consider the following two-dimensional linear dynamical system, % 2 10 8 :61 ﬂ —8 —10 £132. dt 1. What is the trace and determinant of this system? 2. Find the eigen values and eigen vector...
Given Problem- . Describe all least squares solutions of the system (-1 7) and then determine the least squares solution with smallest Euclidean norm. You may work directly with the normal equatio...
Given Problem- . Let A = Use an SVD to determine orthonormal bases of the four fundamental subspaces of A (unless a subspace is trivial, i.c., equals {0}.) You can use Matlab to determine an SVD o...
Given Problem- . 1. Four observations; are given for the data. to, 31,132. These are recorded in the following table: b (11 (12 1 1 D 2 ﬂ 1 U 1 1 —1 2 —1 Determine the best least squares ﬁ...
Full steps on paper please. Graph paper only here if needed. . 5. For each of the following functions, a) Determine the equation of the inverse. b) State whether the inverse is a function or not. If ...
Please show it step by step. Thanks!!. 1. Consider the function f : R2 - R given by f(x) = T, ter-21. (a) Find the gradient of f. (b) Find the Taylor approximation f of f near the point = = (1, 2). (c...
Hi i need help with the problems highlighted and circled in red, its only linear algebra . 176 CHAPTER 2 Matrices and Linear Transformations 4. Give the domain and codomain of the matrix transfor...
. If A E Rnxn has n distinct eigenvalues and commutes with a given matrix B E Rnxn, show that 1. B is diagonalizable. 2. There exist coefficients ao, a1, ..., an-1 such that B = an-1An-1+ an-2An-2+ ...
. Are the following statements true or false? If true, prove the statement. If false, give a counterexample. 1. Let A E Rnxn. If A2 : A, then eigenvalues of A are either 0 or 1. 2. Let A E Rm": If...
Page 2 of 4 1: 2022 MATH 163 . Let O and B = 9 -1 11 Find the values of x and y such that A = B. [3] 3. A = 2 9. B - B 4 4. C- o N LO LNL and D = [2 2 ] Evaluate the following 1. (3 marks) A - 3B 2. (...
. 5. The revenue generated by sales in the Vancouver and Quebec branches of the A-Plus auto parts store (see Example 2) was as follows: If the Canadian dollar was worth $0.65 U.S. at the Vancouver Q...
. Use the Hecht-Nielsen (H-N) function (eq 1) to calculate the H-N value using the initial state vector (1, -1, 1, 1, -1) and the weight matrix below: Equation 1: Hard limiting function: H-N =->w...
. Consider the system, it dac =(1-r)x - x2, r ER, r ER. which statement is true? O the system exhibits a supercritical pitchfork bifurcation at r = 0. the system exhibits a transcritical bifurcation...
. Let R C S x S be any binary relation on a set S. Consider the sequence of relations R", R', R-,..., defined as follows: I = {(x, x) : xES}, and 1= R" U (R; R" ) for n 2 0 (a) Prove ...
Section 3.1 Vector Spaces: Problem 5 (1 point) Let V = R. For u, v E V and a E R define vector addition by u E v := u + v - 3 and scalar multiplication by a Du := au - 3a + 3. It can be shown that (V,...
. (1 point) Assume that A is a matrix with four rows. Find the elementary matrix E such that E A gives the matrix resulting from A after the given row operation is performed. Then find E- and its de...
. Given nonzero vectors x, y E R", the vector projection p of x onto y satisfies the following properties: (Select all that apply.) Op = ky for some scalar k. v pix. v X = p +z for some Z with ...
For f ( x ) = x3 -x2 - 8x + 12 x2 - 9 , show your work for steps "0 to 6" to identify the characteristics as we have done in class (see lesson 3-3). Justify the behaviour of the function nea...
As I am very familiar with the system, please read the instructions below question and kindly follow each single one of them : -If you are not ( proficient with Masters' or above in the subject, ple...
. 2. [10 marks] Consider the plane given by To : 2x - 4y - 2 = -1. (a) Determine whether the plane wo is parallel or perpendicular (or neither) to the line given by (b) Determine the distance betwee...
. 8. [4 marks] Consider the polynomial p(x) = x - 3x + 2. Suppose that B is an n x n matrix satisfying the polynomial equation; i.c., p (B) =0. Prove that B-exists, and find an expression for B- (in...
. 0 2. Let A= -2 , and let b = NON (a) Write the augmented matrix of the linear system AT = b. (b) Apply the Gauss-Jordan algorithm to find the reduced row echelon form (RREF) of the augmented matri...
As I am very familiar with the system, please read the instructions below question and kindly follow each single one of them : -If you are not ( proficient with Masters' or above in the subject, ple...
Please answer and show work for numbers 1,5, and 6. Section 10.4 Problems In each of Problems 1-6, determine whether S is a sub- space of Rn. 1. S consists of all scalar multiples of < -2, 1, -1,4 ...
A car rental company charges an initial fee plus an additional fee for each mile driven. The charge depends on the type of car: economy or luxury. The charge E (in dollars) to rent an economy car is g...
Hawaii Sugar Company produces brown sugar, processed (white) sugar, powdered sugar and molasses from sugar cane syrup. The company purchases 4000 tons of syrup weekly and is contracted to deliver at l...
Homework question. Does the Extreme Value Theorem apply to the maximization problem (2)? Explain why or why not, and if yes, also state what the Extreme Value Theorem implies for this problem....
1. 2. 3. 4. 5. . Explore the effect of an elementary row operation on the determinant of a matrix. State the row operation and describe how it affects the determinant. 6 7 B b 6 8 What is the ...
. Q5. Determine if each of the following operators L: V -> V is diagonalizable. If L is diagonaliz- able, give a basis D for V with respect to which [LID is a diagonal matrix and write down the d...
. 1. Use row operations to compute det(T): a a- T = b 62 1 c C 2 2. Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1,0, - 2), (1,2,4), and (7,1,0). Ske...
. - 2 (e) 2 NAO ([) -3 g -6 (h) (i) 3. Question 9 1 pts For problem 1e, how many distinct eigenvalues are there? Enter the correct digit. Question 10 1 pts For problem 1e, how many linearly independ...
. matrices. (a) - 2 3 9 (b) (c) 7 1 (d) 7 1 7. Question 5 1 pts For problem 1c, how many distinct eigenvalues are there? Enter the correct digit. Question 6 1 pts For problem 1c, how many linearly i...
. Let A c Rmxa, m > n, and be R" be given and suppose that A has full column rank. a) Let Q, R = [A b] e Rmx(n+1) be the reduced QR factorization of the extended matrix A = [A b]. Let us fur...
3. Let A= A1 A2 ... An be an n x n matrix, where A; denotes the i-th column of A, for 1 < i < n. Suppose there exist real numbers 02, 03, . .. , On such that A1 = 02A2 + 03A3 + ... + OnAn. Show ...
1. Show the determinant of the following matrix.(20 Scores) +NON NONH HNDH O 2. Solve the following equation system. (20 Scores) a, taz + a 3 + a = 0 80, +4a2 + 2a3 + a =-2 27a, + 9a, + 3a3 + as = 2 6...
As I am very familiar with the system, please read the instructions below question and kindly follow each single one of them : -If you are not ( proficient with Masters' or above in the subject, ple...
IT. (10 points) If A and B are 2 x 2 matrices, det(A) = 2, det (B) = -7, then det( AB) = det (-3A) = det ( AT B3 ) = det ( A2 B-]) = det(-3ABT A-1) = Note: You can earn partial credit on this problem.
Please help, will definitely upvote. . Change of Basis {a} {b} (C) {d} For any given vector, we have to choose a basis to write this vector in. Typically, we choose the standard basis { e1, e2, . . ...
. Find all values of / for which det(A) = 0, using the method of this section. 1- 6 0 0 A = 0 4 0 5 1-1 M = AZ= 1= = i Fill the upper blank with the greater value of A if it exists. Fill the blank w...
. Find all values of A for which det(A) = 0, using the method of this section. 1 - 4 A = -11 1+8 M1= 12 = Fill the upper blank with the greater value of A if it exists. Fill the blank with the symbo...
. Question 6: Let S be the fixed matrix S = W N. Let be the standard basis for M2x2, and let be another basis for M2x2. Define the linear transformation T : M2x2 -> M2x2 by T(A) = SAS-1. (a) Find...
. WW6.1: Problem 3 Previous Problem Problem List Next Problem (1 point) Let {e1, e2, e3, e4, es, e } be the standard basis in R". Find the length of the vector = = -2e1 + 5e2 - 4es - 5e4 - 3es ...
I need the Answers for all of them . Math 2318, Fall 2022 Graded Assignment III- Due Wednesday October 26th, 2022 Note: all calculations are to be done BY HAND-no "shortcuts" on calculat...
. (1) Find all s ( R so that r - sr + 8 = 0 has two real solutions. (2) Prove that for all r, y ER, we have &ry3 < (2x + 3)2. (3) Let f : R -+ R be defined by f(x) =5x* -7x - 10. Prove that i...
. Use the given inverse of the coefficient matrix to solve the following system. 5X1 +2X2 = - 8 A = -6X1 - 2X2 = 4 3 Select the correct choice below and, if necessary, fill in the answer...
. Question 1 Let 60 -67 37 A = 45 -51 27 26 -29 13 -4 -38 42 -26, and let V = RS. Define a linear operator T : V - V, T(x) = Ax. (a) Explain why if 1 is an eigenvalue of A with corresponding eige...
Problem 6: Let A be the line y = -5x + 2. For each property of a subspace, prove or disprove that A satisfies it. Is A a subspace of R2? Using all of the below: (a) zero vector belongs to A? (b) closu...
. Exercise 1 (8 pts) Let a, B, y, d E R. Denote A = (a . Show that TA : R' - R' where v I A.v is a linear map. Similarly show that for A ( Mmx(F), TA : F" - F" where v - A . v (matrix mult...
As I am very familiar with the system, please read the instructions below question and kindly follow each single one of them : If you are not ( proficient with Masters's or above in the subject, ple...
. WW5.4: Problem 5 Previous Problem Problem List Next Problem (1 point) Suppose that a 2 x 2 matrix A has an eigenvalue 2 with corresponding eigenvector 3 2 and an eigenvalue -2 with corresponding e...
. WW5.4: Problem 3 Previous Problem Problem List Next Problem (1 point) Let 3 6 A 0 3 If possible, find an invertible matrix P so that D = P-AP is a diagonal matrix. If it is not possible, enter the...
Question below. 3. Draw 3 diagrams illustrating what a parabola would look like with the following number of roots. Describe what you know about the discriminant for each diagram. 6mks a. 2 roots b. 1...
The question below. 2. Using the base equation of y = x2, determine the how the following translations affect the equation in VERTEX FORM. y = a(x - p)+ q. 4mks a. Translate 4 units up b. Translates 2...
. 38. Let A be the matrix given in Exercise 26. a) For each vector b that follows, determine whether b is in R(A). b) If b is in R(A), then exhibit a vector x in R2 such that Ax = b. c) If b is in R...
only the circled one . 8:56 3.3 EXERCISES Exercises 1-11 refer to the vectors in Eq. (14). a = d -37 --[8 ] (14) In Exercises 1-11, either show that Sp(S) = R2 or give an algebraic specification ...
. WW5.2: Problem 4 Previous Problem Problem List Next Problem (1 point) Find the eigenvalues of the matrix 1 2 C = -2 -3 1 2 2 The eigenvalues are (Enter your answers as a comma separated list. The ...
. {1 point) The matrix 4G I] D —31 E 5 —1 —1 —1ﬂ —Q 1 1 14 13 has two distinct real eigenvalues .11 w: Jig. Find the eigenvalues and a basis for each eigenspace. The smaller eigenvalue ....
. WW5.1: Problem 3 Previous Problem Problem List Next Problem (1 point) The matrix 2 0 0 A = -10 4 8 8 4 -8 has eigenvalues -4, 0, and 2. Find its eigenvectors. The eigenvalue -4 has associated eige...
Find the LU factorization of A = ⎣ ⎢ ⎡ − 1 4 − 2 3 − 5 1 8 − 4 1 7 − 1 0 ⎦ ⎥ ⎤ A = ⎣ ⎢ ⎡ ? ? ? ? ? ? ? ? ? ⎦ ⎥ ⎤ ⎣ ?...
Find the LU factorization of A= [ 1 5 − 2 − 1 2 ] and use it to solve the system [ 1 5 − 2 − 1 2 ] [ x 1 x 2 ] = ∣ ∣ ∣ ∣ ∣ − 1 0 − 5 6 ∣ ∣...
. 3 75 Let U1 = 4 , U2 = 50 be a basis for IR . Use the Gram-Schmidt process to O 50 2 find an orthogonal basis under the Euclidean inner product. 72 Orthogonal basis: V1 4 V2 = 54 , V3 50 a EX: 1.2...
what would be a relation problem? I know now with tutor that is is a function problem. my question is how would this look different as a relation. im a visual learner. Consider this equation: f(X)=2x ...
. Question 38 (1 point) What is the degree of the polynomial p(x) = (23 - 3)3(202 + 220 + 5) 4( 3x + 1)3 ? Question 39 (1 point) How many non-zero bits are in the binary expansion of 222 - 212 ? Que...
. Question 22 (1 point) 3758. The number 14121237 is composite and thus will have a prime factor between 2 and True False Question 23 (1 point) - 126 True False One Point Multiple Choice Questions A...
. Question 50 (3 points) What is the closed form for the solution of co an - an-1 + 2an-2; do = 2, a1 = 7 ? O < > an = 3 . 2" - (-1) " O an = 3 . 2" + (- 1) " O an = -2&quo...
Eigenvalues of symmetric matrices . 1. Let A be a symmetric matrix. Let v1 be an eigenvector of A with eigenvalue )1, and let v2 be an eigenvector of A with eigenvalue 12. Assume that A1 * 12. Prove...
Properties of Upper Triangular . 1. Prove the set of all lower triangular matrices is closed under matrix multiplication. 2. Let U be an square n X no lower triangular matrix. Prove that the determi...
. Question 5 3 3 3 Let A = 10 -2 -8 , and let B = A*A, a normal matrix. 5 -11 6 (a) Prove that the eigenvalues of B are 200, 150, 27, and illustrate the property of normal matrices by finding a unit...
Question 5 The Demarco's bought a home 9 years ago by taking out a loan for $170000. The interest rate was 5.1 % interest compounded monthly for 20 years. Their monthly payments are $1131.34 and they ...
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. . State which property of determinants is illustrated in this equation. 6 0 O - 12 9 6 - 12 9 6 E - - 6 0 0 -2 -9 -7 -2 -9 -7 Choose the co...
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.. Compute the determinant using a cofactor expansion across the first row. Also compute the determinant by a cofactor expansion down the second co...
. 5. Consider Newton's method for solving the nonlinear equation ﬂm) = :32 — a = 0 Where a > 0 whose two roots are :tﬁ. (a) Should the iterates {xn} for satisfy 1 xn+1 : §($n —|— a/x...
. Show ALL details to get credits. Missing details will result in points off even if the answer is correct. A 0 point will be entered if no or almost no details are provided even if the answer is co...
. Given the following matrix: 2 2 A = 1 3 -1 , = 5 is an eigenvalue of A. -1 -2 2 Find the eigenvectors of A corresponding to 1 = 5. entry 1 Express the answer in a vector form as entry 2 and use t ...
A = [0,0,0,0,1;0,0,0,1,1] B = [0,1,0,1,1;0,0,1,0,1;0,1,1,1,1;0,0,0,1,1] a) what rows in B gives vectors in the solution space of A. b) which vectors are in the row space of A. calculator can be u...
The cost, C dollars, for a long distance phone plan with numbers of minuets, m , with bell is a $6 package fee plus 10 cents per minute. At sprint, the cost is 15 cents per minuet with no package fee....
Please answer the following. Put a solution if it's okay, thank you! . D Question 8 3 Find the inverse of A. Use manual computations ONLY. No Matlab please. 2 2 A = 0 2 O A has no inverse. O A I = O ...
Please provide a table with the initial word problem, restrctions, restriction inequalities, feasible sex, equation, and answer. Thank you. . Investment Planning Mr. Jones has $9000 to invest in thre...
. WW4.5-4.6: Problem 2 Previous Problem Problem List Next Problem (1 point) Find a basis of the subspace of 1R defined by the equation 2c1 - 312 + 4x; = 0. Basis: E. {1 point) Find the dimensions of...
sheet to receive credit for a problem. No points for answer only. Finance Formula Sheet pdf 1. (4 pts) Suppose you paid $87.69 for an item that was 16% off the original price. What was the original pr...
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