2 Find the matrix of the quadratic form 2x1 + 3x22 – x32- 4x1x2-2 x1X3 +6 x2X3 2 -1 2 -2 1 (a) 3. 3 (b) -2 3 3. -1 3 -1 -1 2 -1] [2 1 -3 -2 -1 (c) (d) 3 3 -1 11 -3 a O e.None of these O C O d O b O

Q: s elect the matrix correspon ding to the form Q(Xi, Xz,Xq, Xu ) = - 2x1² + 5 x - 7X -4 Xu - 6Xi Xz +…

A:

Q: 3. Solve the following systems of equations using Gaussian elimination. (f) 2x, – 3x, - X = = Er 3x,…

A: The Gaussian Elimination method is Also known as row reduction to find solution of system of linear…

Q: 16. find a QR factorization of the T O I Į 35 -3 1 2 ما ما له 5 5 3 2. 8 matrix

A: Given is the matrix: 135-1-31023152158 We will find the QR factorization using Gram-Smidth method.

Q: Which of the following matrices of rationals is in reduced row- echelon form? 1 0 0 -3 1 (a) 1 4 (b)…

A: As per Bartleby guidelines we're supported to answer only one question when two or more different…

Q: 6. Find the matrix of the quadratic form. Assume x is in R³. a. 3x} – 2x3 + 5.x + 4x1x2 – 6x1X3 b.…

A:

Q: Find the matrix of the quadratic form 2x12 + 3x22 – x32 – 4x1x2 - 2 x1X3 + 6 x2x3 2 2 -1 2 -2 1 (a)…

A: We have to find Matrix of the given Quadratic form.

Q: 1. Find the totally positive QR-factorization of the matrix 1 0 0 1 0 1 A = 1 1 1 1 1 1

A: Given matrix is: A=100110111111 A=Q·R…

Q: 2. Suppose that A is a 3 x 3 matrix that satisfies A = A 12 (a) Show that the rank of A is at most…

A:

Q: 2. Let 2 25 IO -1 23 7 013 and B= 32-1 23-2 A = a) If possible, invert the matnx A b) then solve the…

A:

Q: 3. Solve the following systems of equations using Gaussian elimination. (f) 2x, 3x2 - X3 2 3x1 5x2…

A: Consider the given equation. 2x1-3x2-x3=23x1-5x2-2x3=-19x1+6x2+4x3=1 Now, make the equations in a…

Q: Solve the matrix equation for X. -1 -2 -4 2 1-4 Let A =2 00 and B = 011B 4B - 4A = X %3D 1-2 2 02…

A: Now, we need to find the expression X = 4B - 4A. So,            X=4B-4A  =4-1-2-4 011 202-421-4 200…

Q: Invert the following matrix 3x – 2y = 9 -x + 3y = 3

A: Solution: Consider the given system of equations: 3x - 2y = 9-x + 3y = 3 The coefficient matrix of…

Q: Solve the initial value problem for the linear system æ' = Ax in dimension 3, where 7 -1 -1 A = |1 5…

A: To solve the initial value problem

Q: 2. Perform the row operation on the matrix. Multiply R, by -7. 0-1 4 -10 -7 3 9. -6 0 -1 42 -0 7. 7…

A: See the solution below.

Q: .1 Suppose A is a matrix with characteristic polynomial CA(x) = x²(x – 1)³(x+2)². Determine the…

A: The solution are next step

Q: (b) Find a real symmetric matrix C of the quadratic form: Q(x1, x2, x3) = x+ 4x3+ 6x3+ 2x1x2…

A:

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

A:

Q: -4 9. 15 Show that A = -1 1 and B = 3 are similar matrices by finding an invertible matrix P…

A: A matrix A is similar to another matrix B when their determinant is the same, their characteristic…

Q: The matrix 1 0 1 -1 1 1 1 0 1 [ −1 1 1] has no QR factorization. O True O False

A: We have to determine the following statement is true or false ; The matrix  101-111101-111  has no…

Q: 5. Suppose that the augmented coefficient matrix of Ar = b is (1 3 1 -1 0 bị 2 6 1 4 12 3 -2 1 ba 1…

A:

Q: Find the characteristic equation for the matrix A 3 0 0 A = 0 1 -1 0. 1 3 -X3 – 7X? – 16X + 12 = 0…

A: Use the method of characteristic equation to find it as in next step.

Q: (b) Find a real symmetric matrix C of the quadratic form: Q(x1,x2,x3) = xỉ+4x3+6x3+2x1X2+x2x3+3x1x3.…

A:

Q: Find matrix K such that MKN = O if Show complete solution. 1 M = -2 3 1 2 0 0 1 N= 0 8 6 6-1 -4 0 -2…

A: Given- M=14-231-2N=20001-1O=86-66-11-400 To find- K such that MKN=0

Q: 2. Find the values of k for which the matrix B is invertible. -2 B= 0 k 1 3 2 1 4 -1

A:

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

A:

Q: Express the quadratic equation 2x2 + 4xy + 7x – 2y + 8 = 0, in the matrix form x" Ax + Kx +f = 0,…

A:

Q: |2 0 if A=| -3 -2 4 and B= 1 find the Matrix X such that 3A+4X=5B 1 3

A:

Q: [3 Given A = 2 2 1 1 3, find [4 1. the lower triangular matrix. 0. 0. 0. 01 a. 2 -1/3 -2/3 -5 01 С.…

A:

Q: The symmetric matrix corresponding to the quadratic form X1 x2 = x} – 2x1x2 + 2x1x3 – 3x + 4x2x3 –…

A:

Q: (-1 2 (b) Compute p(A) for the given matrix A = and the polynomial p(x)=x² – 2x+1 0 3

A:

Q: Find the matrix of the quadratic form. 2 4x1 + 6x +3x3-10x1x2 + X2X3 Select one: O A. O B. C. O D.…

A:

Q: 2.2.8 Show that if a matrix is positive definite then it is invertible, and its inverse is also…

A:

Q: s elect the matrix correspon dinp to the form QlX, Xz, Xg, Xu ) = - 2x1²+ 5 x² - 7×3 -4Xu -6Xx Xz +k…

A: Use the fact that aij=coefficient of xixj/2 for I not equal to j And aii=coefficient of xi^2

Q: Q3. In the triangular decomposition of a symmetric nxn matrix (in the form of LL"), the number of…

A:

Q: -5 -8 Show that the matrix A = 0 is involutory. 1 -1 3.

A: Definition of Involutory matrix: Let A be a Square matrix, A is involutory if its inverse is same as…

Q: 1 3 Find a QR factorization of the matrix A = 1 4 0 2

A:

Q: Question 44 Select the matrix corresponding to the quadratic form Q (21, 12, 13, 24) = -2xf + 5x –…

A:

Q: s elect the matrix correspon ding to the form Q lXi, X2, Xq, Xu ) = – 2x,²+ 5 x; - 7×5 -4 Xu -6X, Xz…

A:

Q: If A? is a zero matrix, then AT A = 0 is: %3D O a. Not possible unless A is a zero matrix O b. not…

A:

Q: This is Matrix A -2 1 1 3 2 1 1 2 1 1 1 2 -2 1 5 A = 3 1 1 -1 1 2 1 5 1 1. a) find its upper and…

A: a) Given matrix is  A=-211321121112-215311-1121511 To decompose a matrix using Cholesky…

Q: Consider the augmented matrix 1 -1 3 7 -2 -1 -3 3 2 -2 5 Performing Gauss-Jordan elimination on this…

A: Consider the augmented matrix Now, performing Gauss-Jordan elimination method, we’ll try to make…

Q: Solve the matrix equation for X. 3-3 9-8 Let A = 0 4and B = B-X= 3A -3-3B 0 5 %3D 6-9 %3= -3-15 -18…

A: Matrix equation

Q: 10. Find the simetric matrix for the quadratic form Q(x1,x2,x3) = xỉ + 3x + x,x2 – x1x3

A: Since you have asked multiple question, we will solve the first question  for you. If you want 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: the matrix correspon ding to the form s elect QLX,,X2, Xq, Xu ) = – 2x1² + 5 x; - 7×3 -4 Xú -6Xi Xz…

A:

Q: Find the matrix of the quadratic form 2x12 + 3x22 – x32 + 4x1x2 -2 x1x3 + 6x2x3 2 2 -1 2 -2 1 (a) 2…

A: We have to solve given problem:

Q: 1. Use the Gaussian elimination to find the values of C1, C2, C3, C4 in the following matrix…

A: We will create augmented matrix and then using elimination convert coefficient matrix into identity…

Q: [3 Decide whether the matrix A = 0 -3 0 is diagonalizable. If so, find P such that P-1AP L5 is…

A:

Q: Find the characteristic polynomial of the matrix -3 1 A = -3 -1 -3 -4 p(x) =

A: Given problem is :