5. Find a dlagonalizes the fouowing natrlx A, and determine the diagonal matrix D = p'AP matrix p that ortnogonally A = 1- 202 02 021

Q: Suppose A = PRP–1, where P is orthogonal and R is upper triangular. Show that if A is symmetric,…

A: According to the given information suppose, It is required to show that if A is symmetric then R is…

Q: If a 3 × 8 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT.

A:

Q: FIND THE FUNDAMENTAL MATRIX AS WELL AS THE FUND AMENTAR MATRIX ø (6)= I %3D SATISEYING x' = 2 -5 -2

A: Fundamental matrix is formed with linearly independent solution sets of the system. These linearly…

Q: Suppose that A is a 18 x 7 matrix and the null space of A has dimension 3. What is the rank of A?

A: For a m×n matrix, the number of rows is equal to m and the number of column is equal to n .

Q: Find a (2x2) singular matrix A that maps (2, 4) into (3, 1).

A: Singular matrix mean its Determinant is equal to 'zero' .

Q: 32. Construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible.

A: .

Q: If the Reduced echelon form of A-λI is the identity matrix then what is the eigenspace (Eλ)?

A: We need to find the eigenspace (Eλ) if the Reduced echelon form of A-λI is the identity matrix. Note…

Q: Let C be a 5 x 7 matrix with a rank 4. (1) What is the dimension of the solution space of Ax 0?

A:

Q: If A is a real n xn matrix, show that AA" and ATA are similar. (Hint. Start with an SVD for A.)

A:

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

A:

Q: 6. Show that if Q is an orthogonal matrix, then 1 0 %3D 0 Q is also an orthogonal matrix.

A: We have to show that HHt = I

Q: Consider an n x n matrix. Give 3 equivalent conditions for A to be invertible

A: Let A be an n×n matrix. we have to give 3 equivalent condition for A to be invertible. Conditions…

Q: Let A be 7×9 matrix. Knowing that Rank (A) 3. Then Nullity(A) is equal to: ||

A: Rank nullity theorem Let T:V→W  be a linear transformation on finite dimensional vector spaces over…

Q: Suppose A and B are nxn matrix and P is an invertible nxn matrix such that A = P-BP (a) Show that A™…

A: We will use Diagonalization  and proof of first part to find power of matrix

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: why cant we just multiply the 1/det(A) with the transpose of matrix like indicated in the red…

A: I am attaching image so that you understand each and every step.

Q: Suppose that collA) = IR+ 4x7 matrix A has 4 lead terms Then and NCA) = R³ %3D %3D

A:

Q: 8.) If A is an mxn matrix, what are the largest possible value for its rank and the smallest…

A: As per the instruction, we will be answering only the first one. For (8), We have that A is an mxn…

Q: Suppose a 5x4 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…

A: Multiple :    Let  A be 5 × 4 matrix . We have given that , rankA = 3. We need to find , dimension…

Q: Prove that the main diagonal of a skewsymmetric matrix consists entirely of zeros.

A:

Q: Construct a matrix system Ax = b, who has a particular solution Xp |1 and the nullspace of the 3…

A:

Q: Suppose that A is a 5 x 5 matrix which has a null space of dimension 4. The rank of A is rank(A) =

A:

Q: In the LU decomposition of the matrix 4. if the diagonal elements of U are both 1, then 9. the lower…

A: Introduction :We have given a matrix , diagonal elements of the LU decomposition of this matrix are…

Q: A 3x4 matrix A has Rank 1, then dim NUTLA %3D

A: The rank nullity theorem says that if T is a linear transformation form a vector Space V to vector…

Q: A matrix that is both upper and lower. triangular is called diagonal ylgn ihi

A: Upper and lower triagular matrix

Q: Suppose U is mxn matrix. Explain why if U has orthonormal columns, then we must have m greater than…

A: Let U be a m×n matrix.We need to show that if U has orthonormal columns, then we must have m greater…

Q: Suppose a 3x8 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…

A: Ans: Given a 3×8 matrix has a rank 3. We want to find the dimension of the null space, dimension of…

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: 2 Find the cosine of the angle between these two matrices, using the standard matrix inner product…

A: Solution

Q: In the LU decomposition of the matrix if the diagonal elements of U are both 1, then the lower…

A:

Q: Show that ||A||2 =  √(ρ(AA*))  where ρ(AA*) is the spectral radius of the AA* matrix.

A:

Q: If the null space of a 5 × 6 matrix A is 4-dimensional, what is the dimension of the column space of…

A:

Q: Suppose A +A+I-0 where A is a square matrix then A= A -A-I -2A A-I CS Scanned with CamScanner

A: Now we will find A-1 . Where I is identity matrix.

Q: Give am example of a 6×6 positive definite banded matrix A with band width 5 (or semiband width 2)…

A: Example of 6x6 positive definite banded matrix with band width 5  A=…

Q: O Give the matix set and condiition up Matrix. of @Optimize which Boarded Hessian 2 2x²4x 2.…

A: minimum value of the function

Q: Suppose A = UDVT where U and V are n x n matrices with the property that UTU = I and %3D vTV = I,…

A:

Q: Q of similarit Y between The rwationship Su9are matrices is

A: This is the problem of Linear Transfprmation.

Q: IfQ is an orthoganal matrix, prove that d'etc@) = +\

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 10 choose a,b,c,d

A: 1. Option a is wrong as the columns of D are LI hence solution will be unique if exists. 2. Option b…

Q: Is it true that when an n*n matrix whose columns form a basis of R^n, then A is invertible?

A: We shall answer this in next step

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: If A is a skew-symmetric matrix then show that AAT = AT A and A² is symmetric. [Note AT denotes the…

A: We will use definition

Q: Let P be a 3x3 matrix having characteristic roots 21 12 = 0 %3D %3D and 23 = 1. Define Q = 3P3 – P2…

A:

Q: solve for matrix Colfficients A. CCX=l,y=l-),2=0]] 3.CCx=1,y=1,2 =]] CCa--4),-(-1をこ0 CCX=3,y=3,=)…

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: a) In statistical theory, a common requirement is that a matrix be of full rank. That is, the rank…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: (a) Determine a lower triangular matrix L with 1s on its diagonal and D a diagonal matrix with…

A: a The given matrix A=2-10-12-10-12consider a lower triangular matrix L and diagonal matrix D…