10. Find a diagonal matrix A that satisfies the given condition a) b) [9 0 0 A- = |0 4 0 A = |0 -1

Q: Find an invertible matrix Q and a matrix J in Jordan canonical form such that Q-'AQ = J, where 7 1 0…

A: Given matrix is A=710-150106 To determine matrix Q and J

Q: Prove or disprove: For any n×n matrix A, AT A = AAT

A: For any n×n matrix A, ATA=AAT

Q: [2.25] Show that C= {x : Ax <0}, where A is an m × n matrix, has at most one extreme point, the…

A: 2.25)   show that C=x:Ax≤0 where A is an m×n matrix , has at most one extreme point, the origin.…

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

A:

Q: 2.3 Compute the principal square root of each of the llowing positive semidefinite matrices. (b) 2 3…

A: Please find the solution in next step

Q: 27. Consider an n × m matrix A, a vector v in R", and a vector w in R". Show that (Av) · w = i · (A™…

A:

Q: If the kernel of a 5 x 4 matrix A consists of the zero vector only and if Au = Aw for two vectors v…

A: It is an necessary and sufficient condition for one one function

Q: 2. Suppose A is a square matrix. Which matrix is not symmetric? O A+AT O AAT ОА-АТ O ATA

A: Note the following results if A and B are two matrices ABT=BTAT…

Q: Consider the Az 1 34 17 9 203 2 8 16 6 0 5 /

A: (a) We know that we can find the determinant of the matrix by expanding along any column or row.…

Q: Find the charo cteristica poly no nomi the matrix A = 3. 3. /- P(x) = 1.

A:

Q: 5. Compute the condition number K(A) of the following matrix 1 1+€ 1 1 1 A 1 1 1 1+€ What is k(A) as…

A: Conditional number is κ∞(A)=∥A∥∞·∥A-1∥∞.If matrix A is known to us so ∥A∥∞ is easy to find .First…

Q: 4. Prove that if A is a square matrix, then det(A™ A) = det(AA") %3D

A:

Q: 2. Suppose that A is a 64 × 17 matrix and that the rank of A is 11. What is the dimension of the…

A: The given matrix is A of size 64×17. Also the rank of A is 11. As we know that for any matrix of…

Q: Suppose that A and B are matrices having n rows. Prove that M(A|B) = (MA|MB) for any m ×n matrix M.

A:

Q: 5. Suppose that A is a 3 x 5 matrix, and the rows of A are linearly independent. What is the…

A: A is a 3x5 matrix. And rows of A are linearly independent. So that dimension of range space of Ax…

Q: A = (ai j )is a 3 × 3 matrix, develop the general ex-pression for det(A) by expanding(a) along the…

A: Given: Let A=aij be a 3×3 matrix.  To determine: The general expression for det(A) by expanding  a)…

Q: (2) Let A = UDV" be a SVD of a square matrix A. What is the sum of squares of the singular values,…

A: We find the sum of squares of the singular values in terms of A.

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: **32. Suppose A is an m x n matrix and x e R" satisfies (ATA)x = 0. Prove that Ax = 0. (Hint: What…

A: Here we use property of modular and dot product.

Q: [1 1 Show that the matrix A is not diagonalizable.

A:

Q: 5. Show that if M is a 3 x 3 magic square with weight w, then we can write M as M = Mo + kJ %3D…

A: Given that ,  A       magic square  To show that : We can write as                     Where,  is a…

Q: 4. Consider the 3 x 2 matrix A such that A - and A (a) Write down A. (b) Is A singular? Justify your…

A: 4. The given equations are,A.12=201 and A.21=201

Q: 31. Let A be a 5 ×7 matrix with rank 4. a. What is the dimension of the solution space of Ax = 0? b.…

A:

Q: 2. Verify, without using the matrix for 0(), that [O()]° is the identity matrix 1 0 0 1

A: This is a problem of rotation of the matrix.

Q: 2. Verify Calay-Hamilton theorem for the following matrix: (2 1 -1 A = (3 1 1 0 2

A: Solution:Given        A=21-1310102To findA-λI=0

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

A: Given  A=1203-12-23-2

Q: (1) Suppose the last column of AB consists of all O's but B itself has no column of zeros. Are the…

A: as you are asking multiple questions I have solved first one , please repost with the remaining…

Q: 3 Let be 4mxn & Bnxm Matrixes that meet: AB = 1 m Prove that to the homogeneous system Bx = 0 There…

A:

Q: Find the null space of matrix A which is 1 3 13] 7 3 8 A =-2 -5 -3 0 3 2 6. 24 3 13 1 2. 6 3.

A:

Q: Consider a matrix A, its SVD is A = UZVH, where [300] -1/√2 0 0 1 1/√2 0 Σ -- 0 2 0,V: Lo o 1] -1/√2…

A:

Q: 2 4. Find the matrix A satisfying A and A 1 and write the SVD of A in vector form. [Hint: Start by…

A:

Q: Suppose that A is an invertible matrix with n columns, and entry aij in row i and column j. 1.…

A: Let matrix is A and the entries are aij .

Q: Suppose that Ax=b has no solution and the columns of A are linearly independent. Let t(A) denote the…

A: This is a problem of Linear Transformation.

Q: 7. If a n x n matrix B is obtained from A, using only m number of row interchanges, then det A det B…

A:

Q: 3- If A² [45] [95] 091 (1 find A where A is UPF triangula matrix

A:

Q: 3. Choose the matrix that is equal to the matrix below. 0.82 2 12 4 5 9 19 082 2 0.6 [B] 12 4 10 3…

A:

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: 4. Find a diagonal matrix A that satisfies the given condition. 16 At = 0 81 0 1. 01

A:

Q: Determine the matrix C such that (CT – 21) 1 1 2 2 3

A:

Q: Show that if A is an n × n matrix, then det(AAT ) ≥ 0.

A: Given, A is a n x n matrix. Let AT be the transpose of A. To prove det (AAT) is non-negative.

Q: 29 What numbera in A-L makes A-QA@ possible (where Qis an orthognael matrix and A is an Zero or 1??

A: We shall solve this question by just using the definition of an orthogonal matrix. We know that a…

Q: independent

A:

Q: 5. Show that if M is a 3 x 3 magic square with weight w, then we can write M as M = Mo+ kJ where Mo…

A: M is a 3 x 3 magic square matrix with weight w. We take weight, w=15 The matrix of M is  Add any…

Q: 4. (a) Prove that if A is an n x n invertible matrix that satisfies the equation A2 = A then A is…

A: Given [A] is n×n invertible matrix.  And satisfies A2 = A a) To prove [A] is an identity matrix b)…

Q: 10. Suppose that Ja) - En, a«|k), [3) = E bu |k). Show that %3D and that this means that the matrix…

A: We are given two ket vectors |α⟩ and |β⟩ as a linear combination of the individual unit ket vectors…

Q: 1) Find a diagonal matrix A that satisfies A-2 20,

A: Here, we need to find a diagonal matrix A such that A-2=2004