8) Show that the matrix -1 Bz 1-4 4 -3 -2 is idempotent.

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: et A be tx8 matrix. Knowing that Nullity (A) = 2. The %3D

A: In the given question, the concept of rank plus nullity theorem is applied. Rank plus Nullity…

Q: Can you provide one image or figure of the hermitian matrix?

A:

Q: b) Determine the matrix A for the linear transtormation which means that the vectors Of the room are…

A:

Q: Show that the matrix is not diagonalizable.

A:

Q: Compute the product 0 () 0 (²) as a 2 x 2 matrix. What kind of isometry is this product?

A: Given product is  Oπ5O2π15 where Oθ represents rotation matrix through an angle θ in anti-clockwise…

Q: Find an LUfactorization of the given matrix.

A: To Determine: find an LU factorization of the given matrix  Given: we have a matrix12-3-1…

Q: 2) does the following matrix is orthonormal and orthogonal? Why? R = 2

A: Orthogonal and orthonormal matrix

Q: Prove the theorem: AAT is a symmetric matrix for any matric A.

A:

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

A: .

Q: The multiplicative identity matrix of order 3 is I3 =_______.

A: Let the Identity matrix be…

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: Is it possible for A3 to be an identity matrix without A beinginvertible? Explain.

A: To explain:It is possible for A3 to be an identity matrix without A being invertible.By definition

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: Compute the singular value decomposition (SVD) of 1 2 0 A = 2 1 0 \o 0 . showing all your working…

A:

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: Find the coordinate matrix of x = (−2, 1, 3) in R3 relative to the standard basis S = {(1, 0, 0),…

A: Given: Then,

Q: Due to what property, applied to the matrices and scalars below, do we know that (cd)A = c(dA)?

A:

Q: Express the following matrix as a product of several elemen- tary matrices. 1 3 E 2 3 ||

A:

Q: Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single cell.)…

A:

Q: Find the matrix of the orthogonal projection of R² onto ar + by 0. %3D

A:

Q: If Aand B are invertible matrices of the same order, Then show that AB is invertible matrices.…

A: LHS   =  (AB)-1  RHS  =  B-1A-1 For    (AB)-1  =  B-1A-1 ,   RHS * inverse of LHS = i…

Q: Show that the matrix; is singular

A:

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

A:

Q: Find the rank and nullity of the matrix; then verify that the values obtained satisfy Formula 4 of…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Find all aclh for which the matrix A = [at3 2 b non-singular.

A:

Q: b) If the matrix has an A = PDPT, prove that A is a orthogonal diagonalization šymmetric matrix

A: If the matrix has an orthogonal diagonalization A= PDPT, then to show A is a symmetric matrix…

Q: Due to what property, applied to the matrices and scalars below, do we know that c(A + B) = cA + cB…

A: Given: We have to state which property for c(A + B) = cA + cB and (c + d)A = cA + dA

Q: verify that the matrices and scalars in Exer- cise 1 satisfy the stated properties. (a) (AT)" = A…

A:

Q: Show that the diagonal entries of a Hermitian matrix must be real.

A:

Q: FIND THE FUNDAMENTAL MATRIX AS W ELL AS THE FUNDAMENTAL MATRIX SATISFYING )- I x'= -4 %3D

A: For the solution follow the next steps.

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

A: Solution

Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: Explain transpose AT of the m x n matrix A?

A:

Q: O If A is possi ble value of dim Nul AT ? Please explain an 8x 5 matrix, what is

A:

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

A: Given:

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: What must one do for the given matrix to be idempotent?

A:

Q: Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single celI.)…

A:

Q: Is this statement true or false? EXPLAIN answer with examples, your Every linear transfor mation T:…

A:

Q: If an upper triangular matrix A is singular then at least one diagonal element is zero. O True O…

A: We have to find out

Q: Let A be an 2 x 3 matrix and b be a vector in R" such that the system Ax = b has solution set 0. 0.…

A: Given: The system Ax = b has solution set 395+s30-7+t072.

Q: Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single celI.)…

A: The given matrix is A=15-2401-12-2-104-8

Q: [5 Let B =E dl: Is the matrix B orthogonally diagonalizable? If yes, find a diagonal matrix 2 0…

A:

Q: §8.2, Exercise 4. Let A be a nonzero 3 × 3 matrix such that A? = 0. Show that rank(A) = 1. %3D

A: Given A is a non-zero 3×3 matrix such that  A2=0 To prove the rank of A is 1 For the proof, the…

Q: show that the matrix П (I2 + 03) ® I2 is a projection matrix.

A: A matrix is a set of numbers organized into a predetermined number of rows and columns. The numbers…