Problem 11 (2016 W 1 ***). Prove the Fredholm alternative: Let A be an m x n real matrix and be Rm. Then exactly one of the following must hold: • Ax = b has a solution x. • AT y 0 has a solution y with yb # 0.

Q: 1. Give an example of a 2 x 2 matrix with no inverse ( singular). Show how it become singular 2.…

A:

Q: 21

A:

Q: For which value of x is the following matrix not invertible: 1 1 3x A = 3x 3x 3x 3x 3x O 2 4 O1/3 1

A:

Q: Some of the entries of the 3 x 3 matrix A are known as A -1 1 If det (A) = -–6 and A-1 find x.

A:

Q: 3. Find x such that the matrix A is equal to its own inverse. 2 -3 A %3D 3

A: Given :  The given matrix is   A = -2-33x To find : We have to find x such that the matrix A is…

Q: Ex. 600. Given the 2x2 Matrix A 1 2 11 3 Determine B=A+A and C=A-A Answers:…

A:

Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z2 – 2xy – 2xz –…

A: Step:-1 Given quadratic form is  Q=2x2 +2y2 +2z2 -2xy -2xz -2yz Q=xyz 2-1-1-12-1-1-12 xyzQ=XTAXHere,…

Q: 1. Find the general solution of x =x2 – x1 + t, x, =x2. 1 2 3 2. Explain why we cannot aclculate the…

A:

Q: 5. Let D be a non-singular matrix such that 7. (7D)- 1 -2 Find D.

A: Inverse matrices

Q: 3. Let A = AB = 1₂. [1 1 1 LO 1 1 1]. Construct a 4 × 2 matrix B using only 1 and 0 as entries, such…

A:

Q: Place the smallest number of zeros in a 4 by 4 matrix that will guarantee det A = 0. Place as many…

A: In linear algebra, the determinant of a matrix is a scalar value that provides important information…

Q: 4. (a) Suppose that A and B are invertible matrices and c is a scalar. Solve the following equation…

A:

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: For which value of x is the following matrix not invertible: 1 1 2x A = 1 2x 2x 2x 2x 2x 4 1 -1 1 2

A: For a matrix A to not be invertible: dat(A) = 0.

Q: .2) x(n)= n2+10 LTI h(n) ho, hỗ y(n)=10 1- By using 2x2 square input matrix, find h, and hy 2- Find…

A:

Q: Find a 2x2 matrix A such that A2 = 1

A: As per the instruction, we will be answering the first question. For (1), We need to find a matrix A…

Q: 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…

A: We state the theorem and explain it with the help of the given matrix A.

Q: Let A =mnd B- then the matrix (2AB + A")" is equal to O None of these O equal to the above 2 17

A:

Q: 15. If A=| B = 0 1 and C = |1 0 then find the matrix (Av B) 0 c

A:

Q: 2. Find a real 2 × 2 matrix A (other than A =I) such that Aº = I . %3D

A:

Q: 1 1 2 Q1. If [A]=3 k1where k is constant. %3D 4 2k i) For what value(s) of k the matrix A has an…

A: For Inverse to exist determinant should be non-zero.

Q: Q2. Apply PA= LU to determine the following matrix A is nonsingular and find A-1: [1 -- -1 A = 2 3…

A:

Q: x-2 1. A= 3x-6 4x-11 Given that the matrix A is singular, find the possible values of x.

A:

Q: 3.a Find the values of x E R so that the matrix A 3 0 0 0 x 2 0 2 x  is positive definite. b. Find…

A: The solution is given by using cholesky's decomposition as follows

Q: 1. Write down the 3 × 2 matrix A with aij 2ij – cos 3

A:

Q: If A E Mpx, (C) nXn is a square matrix, and B is unitarily similar to А, then A and В have the same…

A:

Q: 5. Find the cofactors and the adjoint matrix of A where (1 1 -1 b) A =|2 3 7 0 -1 a) A =-2 0 -2 4 -3…

A:

Q: Solve the following equation involving a determinant. If y multiple answers, enter them as a list,…

A:

Q: 1. Use matrix inversion to solve for x, y, and z if: x + 2y + 2z = −1 y − x − z = 0 2z + 3y + 3x = 1

A: see below the answer

Q: Find the value of x if the matnx 1 5] 4 is Singular 2. A = -3 6. 2

A: