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

Q: 4. Find a real-valued fundamental matrix for y' = Ay where [2 1 0 0 2 0 |0 1 A =

A: Given: A=210020012

Q: The mist Consider ann x m matrix A. Find dim(im(A)) + dim(ker(A")), in terms of m and n.

A: Please check step 2 for the solution.!

Q: Let E and F be n × n elementary matrices and let C = EF. Is C nonsingular? Explain.

A: Let E and F are elementary matrices and let

Q: Find the elementary matrix E such that EC = A where 2 1 5 2 1 A = 3 0 -1 and C- 3 Communest 0 6 -8 2…

A:

Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

Q: Find the steady-state vector for the matrix below. 0.3 0.5 0.5 P= 0.2 0 0.2 0.5 0.5 0.3 (Type an…

A:

Q: [3 Compute the natrix exponential e4t for the diagonal matrix A = !!

A:

Q: CD, where C and D are n x n matrices and C is invertible. Prove that the matrix product DC is…

A:

Q: Let A be symmetric matrix. Then two distinct eigenvectors are orthogonal. False O True

A:

Q: Let A be a matrix with singular values {1, 2, 3,..., 2022}. Find the singular values of the matrix…

A: Given,     A = [ 1, 2, 3, 4, . . . . . . , 2022]

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: Consider the Az 1 34 17 9 203 2 8 16 6 0 5 /

A: (a) We know that we can find the determinant of the matrix by expanding along any column or row.…

Q: An n x n matrix A is orthogonal if AA" = I. If A is orthogonal show that det(A) = ±1.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Let A be a nonsingular matrix. Show that det(A−1) = 1/det(A)

A:

Q: (2) Consider the matrix -[: ] A = Find the unique x, y E R, such that A? = xA – yI (where I…

A:

Q: A. Find the determonant of the matrix A 1 2 1 -21 -1 -2 -1 4 2 1 3 2 -2 1 2 -3

A: Given :A=121-2-1-2-142132-212-3

Q: e' Let M = be a fundamental matrix for the system X'= AX. Find the exponential 3e matrix eAt

A: Given :           M = et03ete2t is the fundamental matrix for the system X' = AX. To find :…

Q: 4. Prove that if A is a square matrix, then det(A™ A) = det(AA") %3D

A:

Q: Let a, b, c, d, e, f, g, h be arbitrary numbers. Show that the matrix а 0 0 b 0 0 0 d A = 0 0 e f 0…

A: Shown below

Q: Suppose A is a matrix such that A² + A = I, I is the identity matrix. Show that a) A must be square.…

A:

Q: tet A be an mxn matrix Prove that on

A: Let A be an m×n matrix prove that Frobenis norm : AF=∑i=1m∑j=1naij212↔·2 on Cmn

Q: compute e^At and e^-At of an identical matrix,I (1  0  0  1)

A:

Q: Find all a,ß>0 so that the matrix 3 2 B [4]= a 5 B 2 1 a is strictly diagonally dominant.

A:

Q: 0. Nrite X = 1 as a product X = E,E,E, of elementary matrices. -1 -1 E, = En = E

A:

Q: 0 0 1. Show that every matrix of the form A = |has an LU-factorization. Does it have an…

A:

Q: Prove the Frobenius theorem in the case where A is a 2 ×2 matrix.

A: This theorem is not valid for order less than 3

Q: I find the cooridinate matrix for A realtive to S=SA, Ag „Az, Au? where A= [2 0 and 1 1 00

A: The coordinates matrix for A is [a b c d]=aA1+bA2+cA3+dA4=A .see 2nd step.

Q: If A is a 2×2 matrix such that trace(A) = det(A) = 3, then %3D value of trace of (A-!) ?

A: Introduction: It is the sum of the diagonal elements of the matrix from upper left to lower right.…

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

A:

Q: Compute det(Ei) if Ei is an elementary matrix of type i.

A: Elementary matrix is the type of matrix which is formed by changing one row of the identity matrix.

Q: If UT = U-1, then matrix U is an orthogonal matrix. %3D O True O False

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: Prove det(A) = det(A'), for an upper triangular matrix A.

A:

Q: A lower triangular matrix of matrix A is c. L = Ex Ek1... E, E,. ... Ek1 E, d. L = E, E, a. L = E,…

A: A lower triangular matrix of matrix A is  .......

Q: If A and B are 3×3 invertible matrices, such that det(A)=2, det(B) =-2. Then det (ABA^T) = ???

A: To solve this problem, we use the standard result of matrix

Q: (iii). If A is ann x n invertible matrix, then show that det(A-1) det A

A: Given that A is an nxn invertible matrixWe know that A.A-1=I

Q: Let B = and B' = Find the change of base matrix from B' to B and from B to B'

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: A is a reversible matrix of nXn. Show that |adjA|=|A|r1

A: As we know that the inverse of a matrix A is : A-1=adj(A)|A|

Q: Assume A and B are two m × n matrices with the same reduced echelon form. Show that there exists an…

A: Given A and B are two m×n matrices with the same reduced echelon form. We have to show that there…

Q: Prove that if E is an elementary matrix, then det(Et) = det(E).

A: Consider two casesCase (1) – If det(A)=0Then by the theorem matrix Ais not invertible this implies…

Q: (a) Show that if A is a square matrix with linearly independent columns, then A+ = A -1• (b) If A is…

A:

Q: - Let A be the n x n matrix with all I's on the diagonal and all 0's above and below the diagonal.…

A:

Q: Let A and B be 0 1 -3 1 2 A = 1 2 B = 0 1 -3 2 2 -1 2 2 -1 | Find an elementary matrix E such that…

A: When we perform a single row operation on this identity matrix we get a matrix known as the…

Q: Let A, Band C be square matrices Such that AB = AC, If A#0,then B-C. 1s this True or false? Explain…

A: Let A, B, and C be square matrices such that AB=AC. If A≠0 , then B=C. Determine true or false.

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

A:

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

A:

Q: Let A be square matrix. I f A"= Onwa for %3D n> 2. Then A= Onun

A: we will see example and conclude.