. Explain what changes in your formula when L is a general invertible lower- triangular matrix and how it reveals that the inverse of a lower-triangular matrix is lower-triangular  b). give a concise proof that the inverse of an upper triangular matrix is upper triangular

Q: (2) Determine all the real numbers a, b, c for which the matrix a 0 b 0 C is not diagonalizable.

A: The given problem is to determine for what values of a,b,c the matrix is not diagonalizable.

Q: a) Is A diagonalizable? Explain. b) If A is diagonalizable, rewrite A as XDX-1 (explain the choice…

A: a) Given            A=310010-310

Q: 1) Show that the real matrix [[0 1 1], [1 0 3], [4 -3 8]] is invertible and determine the inverse…

A:

Q: Is this statement true? It is possible for the square matrix A to be invertible and to have its…

A: Note: The determinant of a square matrix A indicates whether A is invertible or not.Now, det(A)=0 if…

Q: Prove that diagonal matrices are symmetric matrices.

A: Given: diagonal matrices are symmetric matrices

Q: Show that any two rows of a matrix can be interchanged by elementary row transformations of the…

A: According to the question,

Q: Prove that the n × n identity matrix is orthogonal.

A:

Q: Show that the inverse of an invertible lower triangular matrix is lower triangular

A: Given : The matrix A is an invertible lower triangular matrix Then we have to show that A-1 is…

Q: Show that eA is nonsingular for any diagonalizable matrix A.

A:

Q: Let A be a 3 x 5 matrix in which not all entries are zero. (a) What size must the matrix B be for AB…

A:

Q: Suppose that A and B are invertible 2 x 2 matrices such that det(AT) = 2 and det(B) = -2. Let x ER…

A:

Q: Each elementary matrix is invertible, and its inverse is an elementary matrix of the same type

A: Let A be a non-singular matrix of order n. Then, A can be reduced to identity matrix In by a finite…

Q: Q1. (b) Determine whether the statement is true or false, and justify your answer. (a) The product…

A:

Q: All elementary matrices are lower triangular matrices Select one: True False

A: The given statement is False. Because we can get elementry matrix by identity matrix by applying the…

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

A: The given matrix: 0a0b0c0d0 To find its inverse by using the Gauss-Jordan method.

Q: [121] In other words, write A = SDS-¹ = SDSt where D is a diagonal matrix and S is an isome- try.…

A:

Q: Suppose that the square matrix A is invertible. Show that the inverse of A is unique.

A: See below the explanation

Q: Find all matrices B that commute with 1 + i (¹+1) :). 0 A = That is, for which AB = BA.

A: Let B=abcd be the matrix such tghat AB=BA

Q: (1 b) Write a common matrix with a format (5 x2) form, provide a specific numerical example. Write a…

A: For the solution follow the next step.

Q: Prove that the inverse of an orthogonal matrix is orthogonal.

A:

Q: 1 -4-2) s) Let A := -2 3 2 4 -8-5 (a) Show that A is diagonalizable and find a nonsingular P such…

A:

Q: Suppose A is invertible.  Explain AT A is invertible.

A: The transpose of an invertible matrix is also invertible, and its inverse is the transpose of the…

Q: Prove that a matrix with a column of zeros cannot have an inverse.

A: Prove that a matrix with a column of zeros cannot have an inverse.

Q: Show that the matrix 2 1 A = 1 3 2 1 1 1 is invertible, but that A cannot be written as the product…

A: Solve the given problem.

Q: Find the inverse of the matrix if it exists A-[:] 0 4 1 5 5 4 Option 1 Option 2 5 5

A: Solve for the inverse of matrix

Q: -4 -4 -16] A = 16 -18 -56 -4 6 -51 That is, write A = LDU where L is a lower triangular matrix with…

A: We can make some row transformations to find the upper triangular matrix prime U', then from this,…

Q: xplain why A can be changed into I using only row replacements and scaling. (Where are the pivots?)…

A: We have to fill the empty spaces in the given proof.

Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

A:

Q: What is the dimension of the column space of A? What is the dimension of the null space of A? What…

A: In this question, we have given  A be a 13×19 matrix with rank=11 we need to find the followings:…

Q: b) Evaluate det[(2A)-1 (3A")], where A is any invertible (2 x 2) matrix.

A: