Illustrate the Gersgorin theorem by the matrix 2 1+ 2i 0 A = -1 -2 – 2i 1/4 1/41/2 140 12 1/7 1/2 1/4

Q: Use Theorem 1.4.5 to compute the inverse of the following matrix. 13 A = 11 NOTE: Write the elements…

A:

Q: Show that the matrix A= -1 0 0 20 is diagonalizable over the set of real numbers and compute the…

A: Given

Q: Use the inverse matrix method to solve Ax = b below X = (x, +2x, = 3 (2x, – x, = 1

A: Given that  To solve the given system by using inverse matrix method. X1+2x2=3 2x1-x2=1

Q: Find the elementary matrix E such that EC A where [2 4. 2 -1 2. -2 and C = 4 A 2 -1 -2 8 -6 [16 10 E…

A:

Q: Consider the following matrices: 5 10 0 -1 1 5 103 B and C= O 1 0 2 10 -1 3 1 4 Find matrix A so…

A: NOTE: Refresh your page if you can't see any equations. . . find the inverse of C

Q: Show that the matrix A has no inverse. 1 2 4 3 A = 5 6. 2 6. 2 4 9.

A: Given matrix is, A=1204000356262409. The matrix A has no inverse is possible only when the detA=0.…

Q: Show that if B is an n × n matrix with entries in C and  B3=B then B is diagonalisable. Where C is…

A:

Q: 2. А %3D [0.7 0.1 Lo.1 0.7

A:

Q: Compute the matrix exponential e for the following system x' = Ax. x'1 = 10x, - 14x2, x'2 = 2x, - X2…

A: First we will obtain the metrics A from the given system of differential equation then we will…

Q: 2 2 3. Transform the given matrix to RREF -2 1 1 -1

A: The given matrix is; 3 2 2 -2 0 1 1 -1 0. Repost the next question.

Q: State Cayley-Hamilton theorem and prove this for following matrix [1 1 A 1 2 -1 %3D [5 8

A:

Q: 2 if A=| -3 -2 4 and B= 1 ,find the Matrix X such that 3A+4X=5B 1 3

A:

Q: a) Factor the matrix A into the product XDX- where D is diagonal. (-1 -2 2 A = 4 3 -4 -2 b) Verify…

A:

Q: Prove that the quadratic equation A^2 - 3A = 2I hold true for the matrix A =  5  -6  -6        -1…

A: The detailed solution is as follows below:

Q: Which is the matrix inverse to the matrix 2 3 1 3 2 1 1 0 1

A:

Q: Consider the following matrix 1 4 -1 -3 1 -2 2 7 A = 1 0 -1 2 3 5 -3 -5 x2 Ах b, where x = and 1 7 b…

A:

Q: DEMONSTRATE THAT A A-1= A-1A = I      FOR THE MATRIX BELOW     1 -1 2 2 -3 4 1 0 3

A: Given matrix A=1-122-34103 We have to  prove that AA-1=A-1A=I We know that A-1=AdjAA

Q: 1. Show that the matrix 2 1 A = 1 2 -1 -1 is positive definite.

A: Given :- a matrix A  We need to show that a matrix is positive definite. We know that , A symmetric…

Q: Determine the cofactor of 2 in the matrix A = 1 9. 7 4 O-4 3. O -3 2.

A: Cofactor of any element aij is the determinant of the matrix formed by deleting row i and column j…

Q: 3) Identify the element in the matrix. [O 2 4 6 X =0 3 6 9 0 48 12 X2,4 =h X3,2 %3D X3,4 %3D

A: NOTE: Refresh your page if you can't see any equations. . the element at the second row and fourth…

Q: Let Q and Q' be two equivalent quadratic forms with respective n x n matrices A and B. respectively.…

A:

Q: 2 : Find the inverse of the matrix 1 -1 A = 2 -() 3 1 with using the Cayley-Hamilton theorem.

A: The Cayley Hamilton theorem states that every square matrix satisfies its characteristic equation.…

Q: 2. Assuming that all matrices are nxn and invertible, solve for D. CTB-A'BACDA²²B™C-2 = CT

A: We use properties of invertible matrices.

Q: Solve the matrix equation AX = : = B for X Г3 1 0 A = | 2 1 0 – 15 – 10 – 22 B = [3 0 1 X =

A:

Q: • The Matrix B from 3 × 2 at bj = 1 - is го 1. 2 2. 7 3. -1 4. 1 1 -2 2 3 4

A: concept of matrix  bij=1-i/j , the entries of matrix B is b11,b12,b21,b22,b31,b32

Q: How

A:

Q: Show that if a square matrix A satisfies A2 − 4A + I = 0, then A is invertible and A−1 = 4I − A.…

A:

Q: Use Proposition 2.50 to state Jacobi's method and the Gauss-Seidel method in matrix notation for the…

A:

Q: -2 1 To show that the matrix A = -1 1 satisfies its char- 1 -3 2

A:

Q: 1. Show that matrix A is singular 1 2 A= 3 -1 -2 3 -2

A: Given  A=1203-12-23-2

Q: of the following Is the fundamental solution matrix for the coefficient i ? 1

A:

Q: If %3D 1- C What me matrix of An11n5 a positive inverse integers).

A: If we know how to inverse a matrix process we can solve the above question

Q: 2) Find inverse matrix using Gauss Jordan Method if available 2) [3 2 -1 A = |6 2 15 0 1

A:

Q: Using only 0's and l's, find the number n of possible 3 x 3 matrices in row canonical form.

A: We have to make all possible row echelon form ( row canonical matrices ) of 3×3 matrix with 0 and 1…

Q: Consider the matrix A = 0 o 0 0 -2

A:

Q: Solve the matrix equation AX = B for X. 3 1 2 B = 7 A = 4 2 3 10 X3D

A:

Q: Let A and B 5 Find the (1,2)-entry of matrix X 3 -3 given that AX+X=B. 9 3 -1 ||

A: follow netx step

Q: 3 3 , Let M 1 -2 -3 Find c1, C2, and C3 such that M3 +¢¸M² + c2M + C3I3 = 0, where Iz is the…

A:

Q: Given that A and B are 5 x 5 matrices and B is invertible. If det(BAB-1 – 21;) = 7, where %3D Iz is…

A: Let's find.

Q: Question 3. Show that (Ax, y) = (x, A"y) for all n × n complex matrices A and all n-tuples (written…

A:

Q: 1 Use the formula A- = -b to find the inverse of the 2 x 2 matrix, if possible. (If an answer does…

A:

Q: Consider the following matrix and vector: 1 1 A =|-2 0 -3 1 1 -4 and x = X2 6. x3 Given that Ax=0…

A:

Q: Example:5 Verify Cayley-Hamilton theorem for the [5 matrix A= 31 and find its inverse. 2

A:

Q: Show that it is impossible to find two real 2 x 2 matrices A and B such that AB - BA = dI where d…

A: Take A and B are arbitrary matrices and find AB-BA and analyse the diagonal elements

Q: Use Theorem 1.4.5 to compute the inverse of the following matrix. 12 0 A 3 NOTE: Write the elements…

A:

Q: ) Use the theorem in Picture 2 to show that these three matrices are not similar to each other. Make…

A: Theorem  Two similar matrices always have same characteristic polynomials.

Q: Determine the dimension 31 43 -8 21 Ab X of the matrix. AN

A:

Q: 2) Find inverse matrix using Gauss - Jordan Method if available 1) [1 3 41 A = |1 -5 L3 -2 41

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: nd the inverse of the matrix 1 0 -2 1 4 -3 4 oices: 8. -3 1 8 3 1 а. 10 4 1 C. 10 4 1 -7/2 3/2 1/2…

A:

Q: 2 Let A = 1 Compute 6I2 - A and (6I2)A. 3 - 3 61, - A = (Type an integer or decimal for each matrix…

A: