- 10 -20 Let A = 10 22 -10 Find an orthogonal matrix P and a diagonal matrix D such that D= p" AP. 20 -10 P - D =

Q: a Verify that det EA = (det E)(det A), where E is the elementary matrix shown and A =

A: E=1k01  A=abcd

Q: Q3: What 3*3 matrix that will generate Figure2 from Figurel. (1,21 LIRAQIA UC2S)ERSITY (2,5) 2,2)…

A:

Q: 1. Find the cofgctor of 6 in matrix B. 4 り り

A: We will find out the cofactor of 6 for given matrix B.

Q: Find the characteristic equation of the matrix by inspection. 4 2] -6 0 0 6 0 0 5] 4 -9 LO

A:

Q: 1) Construct the matrix A =(a;;) where 3x2 ) aj = i+j, if i = j,and Li-j, if itj %3D

A:

Q: 3 -2 -2 Verify that A s-'AS = diag(1, 2, 23). -3 -2 -6 is diagonalizable and find a matrix S such…

A:

Q: Consider 12 1 2 13 -1-3 4 Convert A to an upper triangular matrix U by using Gaussian elimination…

A: The given matrix, A=121213-1-34 The upper triangular matrix is of the form A=a00bc0def To find a…

Q: 17 17 Find the transpose of the matrix A = | 14 -2 3 13 14 20 AT = %3D

A: Given the matrix

Q: 3 find uB. -4 Find the transition matrix P from the basis B = {(3, -1), (1, 1)} of R2 to the basis…

A:

Q: An n x n matrix A is orthogonal if AA" = I. If A is orthogonal show that det(A) = ±1.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: -14] is a linear combination of the vectors 16 if and only if the matrix equation Az = b has a…

A: Solving

Q: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

Q: 2) Suppose that A and B are nxn matrices that satisfy AB=AB. Show that AB = AB.

A:

Q: Suppose that we use the LU-decomposition of a matrix A as displayed below to solve Ax = b in two…

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Q: 3 0 0 0 1 1 is an elemanter matrix. |\ 0 1 Choose one: true false

A:

Q: 11 A square matrix A is orthogonal if AA" = 1. What properties must be possessed by the columns of…

A: Given:

Q: 1] 1 1 method of SVD provided matrix A = -1 11

A:

Q: It exists, Ol the matrix. 1 - 1 2 – 1 1 1 1 2

A: A-1=?

Q: 2 4 8 Suppose that A = LDU = 039 , then the matrix U is 0 0 7 equal to: 2 00 0 3 0 0 0 7 1 2 4 0 1 3…

A: Given:Suppose A=LDU=248039007To find : Matrix U

Q: 4 9- That is, find an -5. | Diagonalize the matrix A [3 invertible matrix P and a diagonal matrix D…

A: Given matrix A=4-63-5

Q: An orthogonal matrix A and its A1 have identical spectrum. Select one: O True O False

A: "Since you have asked multiple questions, we will solve the first question for you.  If you want…

Q: 4. Let (t) be the special fundamental matrix with (0) = I of the system 7' = A7, whore 4 is an n y n…

A: Consider the equation

Q: -2 2 Let A = Find a matrix P that orthogonally diagonalizes A. Then, verify that 1 the equation P™…

A:

Q: If A is a 3 x 3 matrix with Eigen values, p, q,r then the Eigen values of A"are 1 1 1 (а) -р, —q,—r…

A: Explained below

Q: Consider A = 21 2 1 3 -1 -3 4 Convert A to an upper triangular matrix U by using Gaussian…

A:

Q: 0 0 1. Show that every matrix of the form A = |has an LU-factorization. Does it have an…

A:

Q: 3 2 2 3 1, find the matrix B Such that AB = 5 3 4 3 4 2 1 6 1 5 6 4 , If A = 1

A:

Q: 5. Find a dlagonalizes the focowing matrix Á, and determine the diaganal matrix D = p'AP matrix p…

A:

Q: The order of the single matrix obtained from 1 1 -1 To 1 23 is 1 0 21 -1 0 2 2 0 3 2 (a) 2 x 3

A: Here the order of the matrix needs to find out for both terms. Subtraction and addition won't affect…

Q: 1. Show that matrix A is singular 1 2 A= 3 -1 -2 3 -2

A: Given  A=1203-12-23-2

Q: nd a basis for the nullspace of the matrix. (If there is n basis, enter NONE in any single cell.) 1…

A: Given : A=13-5401-13-2-610-8

Q: [13 5 matrisinin rankının 2 olabilmesi için c aşağıdakilerden hangisi olamaz? 26 c if the given…

A:

Q: 8.) Find the LU-factorization of the following matrix 1 2 2 2 3. 1.

A:

Q: 1. Find the matrix P that projects points in the plane onto the line 5x - 2y = 0

A: As per honor code, we are entitled to solve only one question at a time so I am providing the same.…

Q: (6) Consider the real symmetric matrix (2 1 0 A = 1 1 2 Construct an orthogonal matrix Q of eigen…

A:

Q: (6) Consider the real symmetric matrix (2 1 0 A 1 1 1 1 2 Construct an orthogonal matrix Q of eigen…

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Q: d the third column of A 'without computi 1 be found without computing the other om nted matrix (A…

A: The matrix is given as A=-2-3-2525431218. To determine the third column of A-1 without computing the…

Q: 6. Find all values of a, b, c and d for which A is skew-symmetric 0 2a-3b+c 3a-5b+ 5c) A = -2 0…

A: As per our norms we have to write one question at a time kindly repost remaining questions Q6)

Q: 3) A = [3 Calculate the 10th power of the matrix with the Cayley-Hamilton Theorem.

A: Given:

Q: 9. Find the QR decomposition of matrix 3 1 -2 A = 1 1 1 -1 2 4 where diagonal elements in R are…

A: Given: A=31-2111-124 We knows that A=QR Where Q is orthogonal matrix and R is upper triangular…

Q: 3.1.Let a matrix B is B = FindB6 by using anonsingularmatrix P suchthatD = P¯-"BP is diagonal.

A: We are given: B = 2213 We need to find out B6 using P-1BP. This can be done as follows:

Q: 43 A and B are B,3 matrices where lAl = -3 and IBl =2. Giren this, what is |-2 AD-2|?

A:

Q: 2. Find a single matrix equal to [1 - i 1+0, where i = √-1 (imaginary unit).

A: To find the product of the given 3 matrices.

Q: Determine the dimension 31 43 -8 21 Ab X of the matrix. AN

A:

Q: Find a basis for the Null Space of the the matrix 1 20 2 5 M =|-2 -5 1-1-8 0 -3 3 41

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Q: 5. Find the orthogonal projection of b = (1, –1,2) onto the left null space of the matrix A = 3 -4…

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Q: (3 (4") *) If A is 3 x 3 matrix with det (A) = 3, find det %3D

A:

Q: 5. Show that the condition that the block matrices (8 ) m ( ) A 0 А С and B В can be matrices of the…

A: Given: The block matrices, A00B and AC0B.   To show: The given block matrices can be matrices of the…

Q: (7) (I Let A? = I be an n x n matrix and A# 1. Show that A is diagonalizable.

A: