4. Prove that the product of two upper triangular matrices is always another upper triangular matrix. 1

Q: Show that there is no matrix A E M250x250 with real entries satisfying AAT = -I.

A: Given that A is real ( All entries are real)  square matrix of order 250×250. The trace of any real…

Q: Prove that if both products AB and BA are defined, then AB and BA are square matrices. Assume that A…

A: We want to prove that AB and BA are square matrices

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: Express the invertible matrix (1 2 1 10 1 1 2) 1 as a product of elementary matrices.

A:

Q: Prove Any n by n triangular matrix with main diagonal entriesare all 1 is diagonalizable if and only…

A: Triangular Matrix: A triangular matrix is a square matrix where all the values above or below the…

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

A: Orthogonal and orthonormal matrix

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: (0) Construct two non-zero 3x3 matrices A and B such that for A its rank is greater than its nullity…

A: two non-zero 3×3 matrices A and B such that for A its rank is greater than its nullityand for B…

Q: Which of the following matrices is not in Row Echelon Form (REF)?

A:

Q: 6.* Let C be a nonsingular matrix with 3 rows and 2 columns. Explain why C has a left inverse.

A:

Q: 2 Construct a 3 by 3 nonzero matrix A so that vector is a solution to Ax = 0 -

A:

Q: VýB × VA

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

A:

Q: 3. 3 If A is non singular matrix whose mverse 2. Al = fad A.

A:

Q: TRUE/FALSE Assume that all the given matrices are n × n. If A = O, but Ak = O (where O denotes the…

A: Given:   To Check: A is singular or not Concept: A is singular only when det(A) = 0

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: whether the matrix is in reduce

A: The matrix is given as  , 190-10001500000100000 1. The condition for row echelon form (ref) is The…

Q: Find a sequence of elementary matrices whose product is the given nonsingular matrix.

A:

Q: 4. Determine whether the matrix is nonsingular or singular. 6ive reasont -11 0 3 2-2 1 le

A: When the determinant of the matrix is zero,                      Then the matrix is said to be…

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: (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: 3. Is the trace of the product of two square matrices equal to the product of these two matrices'…

A:

Q: 4. Suppose that a matrix A can be writ

A: Given, a matrix A can be written as the matrix product A=BC as follows:…

Q: Show that any matrix of size 3 by 3, can be written as the sum of two invertible matrices, that is,…

A:

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: 2. If A is an upper triangular matrix and B is a lower triangular matrix, then ((AT)-- 2B)- is : O A…

A:

Q: Ч. W is the set of all 2x2 upper triangular matrices in Mzx2 (IR).

A:

Q: 2 3 Show that the matrix A is singular. 4 6

A: Concept used: Singular matrix are the matrix that is not invertible. In other words the determinant…

Q: 2. Determine the matrix X, such that:

A: Solution:-

Q: Prove that the product of two n x n anti-diagonal matrices is diagonal.

A: To prove that the product of two n*n anti-diagonal matrices is a diagonal 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: 13. a) Show that if A and B are n x n matrices, at least one of which is invertible, then AB and BA…

A: (a) If A and B are two n×n matrices, and one of them is invertible, then show that AB and BA are…

Q: Prove that the product of two upper triangular matrices is always another upper triangular matrix.

A: We have to prove that the product of two upper triangular matrices is always another upper…

Q: If the null space of a 7 × 6 matrix  is 5-dimensional, what is the dimension of the column space of…

A:

Q: 18. Let A be a 3 x 5 matrix with 2 pivots. What is the dimension of Nul(A)?

A:

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

A:

Q: 4 2 If A is a nonsingular matrix whose inverse is find A.

A: If A is a nonsingular matrix whose inverse is 4211. we have to find A.   the inverse of the matrix A…

Q: 4. Prove: If A and B are both n x n matrices, then det(AB)= detAdetB. (Only use 2x2 matrices)

A: Given A and B  n×n  matrices to prove  det(AB)=det A det B

Q: 6. Give an example of two matrices, A and B, neither of which contains any zero entries whose…

A: Below mentioned a example related to this, you can construct many.

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

A: Given:

Q: 7. Show that the matrix A=I– 2vv' , where v is a unit vector in R", and I is an nxn identity matrix,…

A:

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: If M is an upper triangular matrix with integer entries then its eige Select one: O True

A: Introduction: A triangular matrix is a square matrix with all zeros below and/or above the diagonal.…

Q: 7. Prove that ||A|| = omax (A) for a real matrix A.

A: For euclidean norm the norm of matrix A may be defined as follows ∥A∥=sup{⟨Ax,y⟩   :x,y∈Rn,…

Q: - Suppose that A and B arenxn matrices and A is invertible. Invent and prove a theorem that…

A: Solution

Q: 1. Show that the scalar multiple of a diagonal matrix is also a diagonal matrix.

A: Since multiple questions are asked we are answering the first question.