2 If A is diagonalizable then A is diagonalizable. Select one: O True False

Q: Prove that if a, bER and a < b, then |(a, b)| = |[a, b)| = |(a,b]| = b – a. %3D %3D %3D

A:

Q: Let A be an n × n matrix with triangular factorization LU. Show that det(A) = u11u22 · · · unn

A:

Q: If A is diagonalizable and B is diagonalizable, must it be true that AB is diagonalizable? Give a…

A: If A is diagonalizable and B is diagonalizable then it is not necessary for AB to be diagonalizable.…

Q: Show that matsix is not 15 diagonalizable A- 2 -3 2.

A:

Q: Prove that if the rows of A are linearly dependent, then so are the rows of AB.

A: Let us assume that the product AB makes sense. To prove that is if the rows of A are linearly…

Q: IfQ is diagonalizable, then AT also diagonalizable. إختر واحداً:

A: We need to check whether if A is diagonalizable, then A is also diagonalizable.

Q: Let M,xn be a set of squarenx n-matrices. Is the set Mnxn a vector space? Explain. Find 2 different…

A: We find two different basis of M_2×2

Q: is not diagonalizable (by similarity) but is condiagonalizable. 4.6.P2 Show that (a) [ (b) [] is…

A: To show: (a) The matix i10i is not diagonalizable but it is condiagonalizable. (b) The matix 1-111…

Q: Prove that if A is invertible and diagonalizable, then A-1 is also diagonalizable.

A:

Q: If A is diagonalizable then A´is diagonalizable. Select one: O True False

A:

Q: we that Al are matrix norm

A:

Q: Suppose that |u| = 4, and |v| = 5. Prove that 5u + 4v and 5u – 4v are orthogonal. -

A:

Q: Let A E Mnxn(R), show that it is possible to express A as the product, A = PQ where P,Q € Mnxn(R),…

A:

Q: Prove that if A is diagonalizable, so is AT.

A: Given: Matrix A is diagonalizable. To prove: AT is diagonalizable. Concept Used:1) If a matrix A is…

Q: Show that if A is both diagonalizable and invertible, so is A-1.

A:

Q: If A is diagonalizable then A is diagonalizable. Select one: True False

A:

Q: If A is symmetric and invertible and has an LDU factorization, show that U = LT

A: To show: If A is symmetric and invertible and has an LDU factorization, show that U = LT.

Q: Let A be an nxn matrix. Prove that dim(col(A²)) < dim(col(A)).

A: Given: Assume that, A is an n×n matrix.

Q: , counting the multiplicities. Then A is orthogonally diagonalizable.

A: We have to examine that matrix A is orthogonally diagonalizable or not.

Q: linear algebra question.

A:

Q: Findthe Linear Eransfromation whose matrix MT with regard to the base to mec2And the natural ruleto…

A: Given T:C2→C3 be a linear transformation whose corresponding matrix is given  MT=i-i1+i-21-1+2i and…

Q: Find (a) projvu and (b) projuv. Use the Euclidean inner product.u = (1, 2, −1), v = (−1, 2, −1)

A:

Q: 1. If two Hermitian operators A and B commute, show that they can be simultaneously diagonalized.

A: Given :-  If two Hermitian operators A and B commute , then they can be simultaneously diagonalized.

Q: Show that if PER"×" is an orthogonal projector, then P+ = P.

A:

Q: Show that if A is skew symmetric, then the elements on the main diagonal of A are all zero.

A: given that A is skew symmetric

Q: Find ATA and AA". 2 0 1 %3D -1 4 2 (a) ATA 1 1 (b) AAT 21 Which of the products are symmetric?…

A:

Q: (c) 0 is neither diagonalizable nor

A:

Q: if| A - B | = | A + B | . prove that A is orthogonal on B

A: Given, A-B=A+B

Q: Let A = [kaij]nxn, B = [aij]nxn, be an nxn matrices and k be a scalar then det(A) is equal to: *…

A:

Q: If A is invertible and diagonalizable, then A also is diagonalizable. Select one: O True O False

A: Solve for true or false

Q: Suppose A and B are both orthogonally diagonalizable and AB = BA. Explain why AB is also…

A:

Q: Prove that, if A is similar to B, and B is diagonalizable, then A is diagonalizable.

A: Given that A is similar to B and B is diagonalizable.  To find A is diagonalizable.

Q: Supbose A, B and c in vestible matnices , show also invertible AB C is that by baioducing matnix D…

A: Let A-1, B-1 and C-1 denotes the inverses of matrices A, B and C, respectively.Show that ABC is…

Q: If A is invertable then A is diagonalizable. Select one: True O False

A:

Q: Show that if A is both diagonalizable and invertible, then so What does it mean if A is…

A: Introduction: If matrix A is an invertible matrix then every eigenvalue of this matrix non-zero.

Q: Do the Same cardimalityq Eitherr give an between them or show no Such bijcction exists- set [o1] and…

A: It is given that

Q: A square matrix is said to be idempotent if A2= A. Prove that if A is idempotent then 2A-I is…

A: If the square of the matrix is equal to the identity matrix then the matrix is said to be its own…

Q: If A ER2X2 is not diagonalizable, then A is not diagonalizable. True or False? Give an example to…

A:

Q: True or False   Consider the following model, Yi = β0 + β1Xi + ui,E[ui|Xi] = 0,i = 1,...,n…

A: Solution: As per the guidelines first three parts should be answered.

Q: Exercise (7): Find , zdxdydz on [0,1] × [0,2] × [0,3]

A:

Q: If A and B are both invertible, then A + B is invertible.

A: Given that A and B are invertible matrices.   Invertible matrices:   If A is invertible matrix, then…

Q: Exercise 2 Given KB = (X→Y) ^ (Y→Z), and a = (X→Z) Is KB |= a is valid or not?

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

Q: Let A = Show that A can be diagonalised. Then, compute A°.

A: The solution of the problem is given in the next steps.

Q: Verify that P = is an orthogonal matrix. 1/32/3 N3

A: Given the matrix P=23-23132313-23132323We need to check whether the given matrix is orthogonal…

Q: Show that if B is m × n, then BTB is positive semidefinite; and if B is n × n and invertible, then…

A:

Q: If A Is diagonalizable then Is diagonallzat Select one: O True O False

A: We will solve the following

Q: Let X be a centered m x n-matrix. Then cov(X) = XTX. %3D Select one: O True O False

A: It is an important part of statistics . It is widely used .

Q: Let A = %3D

A:

Q: If A EM,C {c} such that A2 = A. Prove that A is not a strictly diagonally matr. the last word is…

A: A square matrix is said to be strictly diagonally Matrix if all entries are zero except diagonal…

Q: Let A= then A is diagonalizable. Select one: True False

A: We have to check