A lower triangular matrix of matrix A is c. L = Ex Ek1... E, E,. ... Ek1 E, d. L = E, E, a. L = E, E2 ... Ek-1 Ek -1 b. L= E, E1. ,E, E, E,1 ... O B O D

Q: For matrix A, B if A – B = O, where O is a null matrix then * A = B B = 0 A = 0

A:

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: If the columns of a 2 x 2 matrix are linearly dependent, what O The space is translated, but not…

A: Here we have If the column of a 2×2 matrix is linearly dependent, then what happen to the space…

Q: Find the characteristic equation of the matrix by inspection. 4 2] -6 0 0 6 0 0 5] 4 -9 LO

A:

Q: Let A = - 2     1    0                 1     0    1                2    -3    1        A is a…

A: trace is the sum of all diagonal elements of the matrix.

Q: determine whether the given matrix A is diagonalizable. Where possible, find a matrix S such that…

A:

Q: Suppose A is a Skew-Hermitian matrix and (a+jb)A is also skew-Hermitian matrix, then O a. a=-1 b.…

A:

Q: Find an LUfactorization of the given matrix.

A: Given, To find LU factorization of the given matrix.

Q: Calculate the matrix P, the matrix D, det(P), and the matrix P! Is the matrix A2 diagonalizable?…

A: Solution:-

Q: Let A be an m×n matrix with rank m and B be an n×p matrix with rank n. Determine the rank of AB.…

A: This can be done as follows:

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 2 -4 A = 4-4 3. - 1 18 -3

A: The LU factorization of a matrix A is writing A as the product of matrices L and U, where L is a…

Q: Consider the state matrix A and input matrix B given by 0. -1 1 1 0 A = -2 1 ;B= 1 1 1 -1 1 2 2) The…

A:

Q: Find the steady-state vector for the matrix below. 0.4 0.1 0.6 0.9 The steady-state vector is (Type…

A: To find - Find the steady-state vector for the matrix below.

Q: Find an orthogonal matrix Q and a diagonal matrix D

A: Follow the procedure given below.

Q: Let A be an m×n matrix and let B be an n×p matrix. Show that if the columns of B are linearly​…

A:

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

A:

Q: If S = A + iB is a Hermitian matrix, are its real and imaginary parts symmetric?

A:

Q: Show that if A is a symmetric matrix, then Ak , k = 2, 3,... , is symmetric.

A: Given that, A is a symmetric matrix. Then we get, A^T = A; where A^T is the transpose of matrix A We…

Q: Let A and B be two skew-symmetric matrices of the same size. Show that AB+BA is symmetric.

A: Given that: Let A and B be two skew-symmetric matrices of the same size. To show: AB+BA is…

Q: If A is a skew-symmetric matrix of order 5 then adj(adj(A5«5)) = %3D

A:

Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

A:

Q: Enter a 3 x 3 symmetric matrix A that has entries au = 5, az2 = 4, a33 = 0, a12 = 2, a3ı = 1, and…

A:

Q: Find the steady-state vector for the matrix below. 0.7 0.2 0.3 0.8 0.4 The steady-state vector is…

A:

Q: Let A be an n ×n matrix and B= A + I, where / is the identity matrix, then it is possible for A and…

A:

Q: Let A be a nonsingular matrix. If det(A)=3, then det(A) = %3D

A: In this question we have to find detA-1.

Q: If the columns of a 2 x 2 matrix are linearly dependent, what happens to space under the associated…

A: Let a 2x2 matrix be A  The columns of A are linearly dependent.

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

A:

Q: Let A be an n x n matrix and let D be a n x n diagonal matrix. Show that AD =…

A:

Q: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

A:

Q: Let x and y be square matrices of order n a. Show that if x and y are skew symmetric, then x + y is…

A:

Q: Let A be an n xn matrix and B= A+I, where I is the identity matrix, then it is possible for A and B…

A:

Q: Let A be an n × n matrix and let B = A + AT and C = A − AT (a) Show that B is symmetric and C is…

A: given: let A be a n×n matrix. B=A+AT C=A-AT we have to show that B is symmetric matrix and C is skew…

Q: Find an LU factorization of the matrix A. 3 -1 3) A- - 18 1 0][ 3 1 A) A= B) A = 10 3 -1 0-3 -6 1 0…

A:

Q: Find a matrix P that orthogonally diagonalizes A, and determine P-'AP. A = 1 4 P = P = 2 V3 V3 2 P =…

A: First we need to find eigen values:

Q: If A is a skew-symmetric matrix of order 5 then adj(adj(A5x5)) =

A:

Q: a b Verify that det EA = (det E)(det A), where E is the elementary matrix shown and A =

A:

Q: A upper triangular matrix of matrix A is a. U = E, E1... E, E, A b. U = E, E,... E, E A c. U = E,"…

A: An upper triangular matrix of matrix A is can be represent as U = EkEk-1........E2E1A This form is…

Q: If U is a square matrix such that UTU I, what can we say about det (U)?

A:

Q: Suppose A is a matrix of order p × q and B is a matrix of order q × r, then illustrate the order of…

A:

Q: The aim of elimination steps in Gauss elimination method is to reduce the coefficient matrix to a)…

A: A matrix where the number of rows is equal to the number of columns is said to be a square matrix…

Q: If A is a 2 x 2 skew symmetric matrix, must det(A) = 0?

A: we have a 2×2 skew symmetric matrix.

Q: Let A be an nxn matrix, and let B be the matrix that results when the rows of A are written in…

A:

Q: A math course has 4 exams weighted 20%, 25%, 25%, and 30%, respectively, toward the final grade.…

A:

Q: If E is an elementary matrix, then ET is an elementary matrix of the same type as E.

A: Both are true statements. a1+2a2-a3 = 0  This means that linear combination of columns or rows is…

Q: Find the transition matrix from the basis B = {(1,2,3) (1,0,1)(1,2,1)} to B' = {(1,1,0)(0,1,1)…

A: