Linear Algebra questions and answers in December 2022

For this question:   This is my work: Is my reasoning correct? I also assume the following is true -- is that correct as well?    . (a) x Ay = (A, xy ) for all & E RM, y e R", Ac Rixn We k...
A company is dedicated to producing tables and chairs. Material costs for each table are 35 and 9.00 for each chair; labor costs are 7 for each table and 3 for each chair; fixed costs are $75 000. The...
How do we know the last inequality, that rank([B I_n 0 A]) \geq rank(A) + rank(B)? This is my current work, where n and m are shared rows between B and A and A and I_n, respectively.  . (b) Using (a)...
A) Describe a real life scenario or problem that could be modelled by a compound or composite function.    B) Explain how the graph models the characteristics and the changes of the real life quanti...
 . 1. Find eigenvalues and eigenvm'Jtors of the following matrices: —1 n A:(1—1)'E: 2. Compute the determinants of the Iriatrices |A|, |E|, from the previous problem, plus the determinant |C I ...
 . Suppose X, Y e C~ with X = ($1, 12, ..., IN), Y = (y1, y2, ..., yN). Denote the usual dot product on C~ by N X . Y = Inyn. 2=1 N (a) Show that (X, Y) = Cn Tryn defines an inner product on CN, if (...
 . Suppose V is a finite dimensional complex vector space. Let T : V - V be a linear map. (a) Suppose v E V is a nonzero vector. If dim(V) = n, show that there is a nonconstant polynomial p(z) of deg...
This is one where I need the question explained. I think i missed the explanation of what adjA means.    Let A be an n x n matrix. If A -1 = (1/(det A))adj A is​ computed, what should AA -1 be equ...
This is one where I need the question explained. I think i missed the explanation of what adjA means.    Let A be an n x n matrix. If A -1 = (1/(det A))adj A is​ computed, what should AA -1 be equ...
   . 4 3. Let S = -1 2 a. Write three vectors of your choice that are in the span of S. 2 b. Determine if each of these vectors is in Span (S) : (i) -5 8 (c) Does the set S (i) span R' (b) form a ba...
 . 3. Answer the following as True or False and justify for answer. (2 marks each) (a) All leading "1"'s in a matrix in row echelon form must occur in different columns. (b) If a linear sys...
 . Q6) Compute the intensity at the centroid of a white triangle with vertices P1, P2 and P3 using the Phong Illumination model considering the following equation: ~ I = laka + li(kaiff (N . L) + Ksp...
LetA=αβT whereα,β∈Rn andβTα̸=0. 1. When will the linear system x ̇ = Ax be asymptotically or marginally stable? 2. Compute eAt.  . 2 Problem 2 Let A = afiT Where a, ,8 E R" and fiTa aé...
TRUE or FALSE: (please give brief explanations)    . 15. There is a unique rank-5 approximation of a given full rank (8x8) matrix. 16. Neglecting extremely small singular values of a matrix produces...
TRUE or FALSE: (please give brief explanations)   1. Solving the normal equations using the Gauss-Seidel method is a good way to solve the least squares problem. 2. An over-determined least squares p...
Are the following statements true or false? If true, prove the statement. If false, give a counterexample. Let A ∈ R n×n be a real symmetric matrix, and λ 1 , λ 2 , ..., λn the eigenvalues of A ...
Are the following statements true or false? If true, prove the statement. If false, give a counterexample. 1. Let A ∈ R 3 × 3 . If each eigenvalue of A is zero, then A 2 = 0 . (Note: 0 denotes the ...
 . 10 5 -5 0 14.14 0 0 0 In a singular value decomposition of matrix A = with > = 0 -5 -5 10 0 10.0 0 0 0.5 -0.71 0.41 0.0 -0.5 0.0 0.82 -0.71 and V= , what is U? -0.5 0.0 0.0 0.71 0.5 0.71 0.41 0...
What is the minimum number of 1's in the adjacency matrix of a connected undirected graph of N vertices (without self-loops) ?    How many 1's are in the adjacency matrix of a complete graph of N ve...
 . -2x - 5y + 2z = -1 -2x + ky + z =2 -x + 2y - z = 2 Above linear system can be solved by using the Cramer's rule: det(Al) det(A2) det (A3) det (A) > y = det(A) det (A) Given det( A3) =42 1. Find...
 . Matrix C is the product of matrices A and B as shown below. AB = C, where -2 1 1 1 6 A = -3 1 5 B = -1 -2 0 and C = 1 5 3 2 0 1 2 y 1 -1 Find the values of x and y. Write solution separated by a c...
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, pl...
 . Question 5 (5 points) _I: A student is trying to solve the linear system by using Gauss-Jordan elimination. They performed some elementary row operations and got to a point where they have followi...
 . Question 3 (5 points) _I: Given the following vectors: u = (2, -4, 0) and v = (1, 0, 3), find: a) u.v [2 marks] b) The angle between u and v (Round your answer to the nearest degree, do not put de...
 . I. (14 points) (a) Let Q be a symmetric matrix. Show that any two eigenvectors of 627 corresponding to distinct eigenvalues, are Q-conjugate. (b) Consider the problem Minimize f(scl, 2:2) = 23% + ...
 . * ( G C O L O L O C ( 1 X IMAC IMA LIM C C C F O L G F G C : C : G F C : C : C: C : G( * E: C : + V X web.whatsapp.com GE Update You today at 10:17 PM X Abishek Katwal Unco Mohsin Math Solve the l...
[3] Consider R3 equipped with the inner product 2 10 d ((a, b,c), (d, e, f)) = [a b c] 1 1 1 e 0 1 3 Using this inner product, find the orthogonal projection of the vector (6, 6,6) onto the plane span...
I just wanted to confirm my answer so I didn't need much explanation. a) Solve the following system of equations using Gauss (or Gauss-Jordan) elimination: -x + 3y +7: =0 3x - y - 5= =0 3x + 2y+= =0 b...
I need help with finding/determining the requirements listed in the bullet points for Parts A - C of the following question. Thank you in advance. I will make sure to rate you well.. 6. For each matri...
 . 4 2 Let u1 0 , U2 = 2 , U3 = be a basis for R . Use the Gram-Schmidt process to find an orthogonal basis under the Euclidean inner product. Orthogonal basis: V1 0 , V2 = a V3 b a = Ex: 5 b = Ex: 5...
Competency In this project, you will demonstrate your mastery of the following competencies: Interpret the properties of vector spaces Utilize advanced matrix techniques to solve complex linear proble...
 . 1. Consider the following second order ODE: y" + 6y' + 9y = 0 (a) Find the general solution by reducing the equation to a system of first order equations: X' = AX (b) Is A diagonalizeable? (c...
 . [6 marks] Let L be a linear mapping with the following matrix representation, which can be reduced to row-echelon form as shown: -2 2—43—1 100: [L]=1—21 0 RREF[L]:010_E 0-614 001—1 (a) Giv...
3D Vectors. I got Vector T right but I can't seem to figure out vector F. . Using the figure below, determine the Cartesian forms of force vectors 1? and I: as |F_'| = 350 N and |QT| = 100 N. |.e., ...
Write the solution in parame. Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given matrix. 0 4 -1 4 -3 0 0 0 O 0 0 0 0 0 0 0 X=X2 + X4 + X6 (Type an integ...
 . Problem 1. In each part solve the morefficent matrix to Reduced Row Ech- matrix you finish with. It's not necessary to show individual mis operations you can just use a machine to find the RREF. 2...
A =  ⎣ ⎢ ⎡ ​ 1 2 1 ​ 3 0 6 ​ 4 3 6 ​ ⎦ ⎥ ⎤ ​ 1. Let a 1 , a 2 , and a 3 be the columns of A, i.e., A = [a 1 a 2 a 3 ], and let W = Span {a 1 , a 2 }. a) Find an orthonormal basi...
 . 3. For the following system of linear equations: x—2y+z=0 x—4z=3 y+3z=7 a) Find A'1 using adjoint theorem [6 marks]. 4. Find det (-2A) if A is a 3 x 3 matrix and determinant of A is det(A) =...
Can someone please explain to me ASAP??!!!!  . The matrix A is equivalent to the echelon form shown below 0 0 15 30 30 1 1 1 1 21 A = -2 -2 37 76 74 ~0 012 2 -1 -1 13 27 26 Lo 0 0 0 0 - N Enter colum...
Can someone please explain to me ASAP??!!!  . 2 2 Suppose T: R2 - R' is given by T(a) = Ax , where A = 2 2 2 Then T ( _ 4]) - (Click in the answer box, select the "Matrix" tab, then choose ...
Answer and explain the following question.  . 3. (10 points) Consider the function X , 0<x<1 f (20) = 0. 1<x<2 Give the Sine Series for f(x). Include the first four nonzero terms. Each co...
Solve the following polynomial equation by grouping and factoring.   36y^3−49y=0   Enter the exact answers.   The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2...
Analyze the graph of the function f(x)=2|x+7|+8 compared to the graph of the absolute value function g(x)=|x| . Shifted    right or left by_______units Shifted    down or up by________units Wh...
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, pl...
  Hello for two questions, I would like to know how to define whether this statement true or false.  Could you show your work in detail? Thanks.    . 2. [2 points] Suppose that A is an m X in, mat...
 . 2. Let A be a matrix of size m x n. Choose the correct statement: (A) A A is always invertible, B) A" A is never invertible, C A" A is invertible if and only if rank A = m, "D) A&qu...
  Hello can you explain why matrix B is not diagonalizable ?. 14. [2 points] For each of the following matrices, write 'Y' if it is diagonalizable, and write 'N' if it is not. You will receive 1 poin...
Please show all the steps, as I want to understand.. MC Question 1 Let A be a 3x3 matrix. Which of the following allows us to conclude that the columns of A are linearly dependent? A. A is symmetric B...
 . 4. i) Determine the "combo matrix" that represents reflection about the x-axis, then stretching along the x-axis by a factor of -2, then stretching along the y-axis by a factor of g and ro...
Can someone please explain to me ASAP??!!. Matrix A is factored in the form PDP -1 Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 8 1 3 0 0 1 2 3 A = 3 5...
Clear handwriting, and Explanation Please. Thanks . Question 6 10 pts 5 1 0 Details Let V = {u, v} where u and v are vectors in R2. What are the possibilities for Span(V)? O The Origin O A line conta...
Following Problem -  (Please don't use the same answer from other website it's confusing) . (a) Let _ 7/5 1/5 A'i4—u9 Determine limn_mo A" by hand. Check your result using Matlab and compute A...
0 -3 4 Let A = O - O - 2 0 N O O (a) The eigenvalues of A are 1 = -3 and 1 = -2. Find a basis for the eigenspace E_3 of A associated to the eigenvalue 1 = -3 and a basis of the eigenspace E_2 of A ass...
(a) For parts (i) and (ii) below, suppose that A is a 4 X 4 matrix with eigenvalues -1, -2, 4 and -3. (i) Find det(A). det( A) = (ii) Is A - 41 an invertible matrix? (No answer given) (b) Suppose that...
-2 You are the given the eigenvectors uj = , U2 = and U3 = 2 of the matrix A given by A = (a) Find the eigenvalues 71 , 12 and 13 of the eigenvectors u1 , U2 and u3 , respectively. M = 12 = 23 = (b) T...
Problem 7. [10 marks] Given the linear operator TA : R2 - R2 defined by 1. Find the standard matrix of TA. 2. Find all eigenvalues and eigenvectors of the matrix A. 3. Present the part 2 geometrically...
Practice 10 1. Given two vertices A(2, - 3, - 5), B (- 1, 3, 2)of the parallelogram ABCD and the intersection point of its diagonals E(4, - 1, 7). Find the coordinates of the remaining vertices of the...
9) Symmetric matrix A = N has eigenvalues ) = 1, 6 with the corresponding eigenvectors - (3). 32 - (12). Orthodiagonalize A, i.e. find the diagonal matrix D, the orthogonal transformation matrix U, an...
Please answer clear, correctly and brief. Projection formula: prat Iw (2 um for orthogonal basis u,. . . , Um of H. 4) Let u = -2), and - a) Find the projection pr, b) Find the distance from a to the ...
1. Explain how a non square matrix could be linearly independent (Since it is not a square matrix we cannot use the determinant). What assertions must hold for a non square matrix to be linearly indep...
  Only 18 and 19 please   . 306 Chapter 4 The Eigenvalue Problem Exercises 20-23 illustrate the Cayley-Hamilton theo- - - -On-2 -di -do rem, which states that if p() is the characteristic poly- nom...
  Only 20 and 21   . Exercises 20-23 illustrate the Cayley Hamilton theo- rem, which states that if p() is the characteristic poly- nomial for A, then p(A) is the zero matrix. (As in Ex- ercise 18,...
Hi there, I have these two questions that I am confused about. I don't need the answers only, I need proper explanations for each answer. All the solutions should be written out in full sentences with...
Can you please explain.. Problem 16. 16. (1 point) the matrix A = - 12 5 has eigenvalues Aj = -1 and 22 = 3. The bases of the eigenspaces are VI = and v2 6 , respectively. Find an invertible matrix S ...
 . 1. Let T: R2 —} R2 be a. linear transformation such that T ([ [1) ]) — |: 3,; ]_. and T ([ [ll ]) — [ 7:; ] (a) (3 points) ["ind the Standard transformation matrix A I'm" T [m that ...