8. Consider the quadratic form 5x,² +2x, +4x,x, (i) Reduce the given form to sum of square form by the means of normalized modal matrix transformation. (ii) Discuss the nature of the given quadratic form.

Q: Suppose A is the 3 x 3 zero matrix (with all zero entries). Describe the solution set of the…

A: To prove  Ax = 0

Q: Find the symmetric matrix A associated with the given quadratic form.…

A: Solution: Consider the given quadratic form is: 2x2 - 3y2 + z2 - 4xz we know that if ϕ =…

Q: 2.3 Compute the principal square root of each of the llowing positive semidefinite matrices. (b) 2 3…

A: Please find the solution in next step

Q: Factorize the matrix into LU decomposition. [0 5 41 A = 5 1 2 1 2 3.

A:

Q: Suppose A is a 6x4 matrix with 4 Pivots. Let T(z) = Ar be a linear transformation from R'into R°. Is…

A: Suppose A is a 6 × 4 matrix with 4 pivots  Let T(x) = Ax be a linear transformation from R4 into R6…

Q: Suppose that an nxn matrix A has a QR-decomposition where

A:

Q: highlighted" condition. A matrix in M2(R) which is “nilpotent" and has a non-zero entry in each row…

A: A matrix is Nilpotent if Ak = 0 where 0 is null matrix and k is index of matrix A.

Q: 2. Find the singular value decomposition of A-() 4 3 -6 8

A: The given matrix  A = 43-68 The singular values of the decomposition are the square root of non zero…

Q: 5. Find the standard matrix representing each given linear transformation. 3u2 |U1 2u1 – U2 2u2 -…

A:

Q: 2 14 Wiite the and system below as Vertor euation. matrix Quatan +6z =0

A:

Q: 8. Identify the factor of the matrix A below using LU decomposition 3 29 218 21 12

A:

Q: 3. 3 If A is non singular matrix whose mverse 2. Al = fad A.

A:

Q: 17. Perform Gaussian Elimin ation on the matrix. [1 4 36 -1 -1 2 4. 0 4 -3-15 6,

A:

Q: -2 1 2 1

A:

Q: If A=XDX−1 where  X is a diagonalizing matrix of A, then 7X is also a diagonalizing matrix of A.…

A: Given: Where, X is a diagonal matrix of A, then 7X is also diagonalizing matrix of A. To determine:…

Q: Find the characteristic equation of the matrix by inspection. 2 -5 9 6 -3 0 0 4 0 0 8

A: Given that: 2-5960-30000400008 The characteristics equation is given by the formulas, detA-λI=0

Q: ГО 5 4 5 1 2 2 3] A = [1

A:

Q: 1. Show that six (or more) lines that have a common line of intersection (a common transversal) are…

A:

Q: 2 4 8 Suppose that A = LDU = 039 , then the matrix U is 0 0 7 equal to: 2 00 0 3 0 0 0 7 1 2 4 0 1 3…

A: Given:Suppose A=LDU=248039007To find : Matrix U

Q: 1 1 -1 6 A : -2 3 2 -4

A:

Q: Find the singular value decompostion of the matrix. 1 1 -1 -1 1

A:

Q: Consider A = 21 2 1 3 -1 -3 4 Convert A to an upper triangular matrix U by using Gaussian…

A:

Q: In the LU decomposition of the matrix 4. if the diagonal elements of U are both 1, then 9. the lower…

A: Introduction :We have given a matrix , diagonal elements of the LU decomposition of this matrix are…

Q: 3. Please compute the LU decomposition by hand for the following matrices. 2 -1 2 100 1 4 1 0 (b). 0…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: 2. Consider the quadratic form Q : R° → R, where Q(x1, 22, x3) = –2x – 8x – 18x3+ 8x1x2 + 4x1x3 +…

A: The given quadratic form is Q(x1,x2,x3)=-2x12-8x22-18x32+8x1x2+4x1x3+4x2x3 The quadratic homogenous…

Q: 4. Suppose B, I – B-' are invertible matrices and (X – A)- = BX-1, find X (as an expression in A,…

A: A matrix Y is said to be invertible if and only if Y-1 Y=Y Y-1=I

Q: 2 3 Show that the matrix A is singular. 4 6

A: Concept used: Singular matrix are the matrix that is not invertible. In other words the determinant…

Q: 2. Find the general matrix output in terms of a, b, c, and d of T(ar³ + bx² + cx + d) when –12 12]…

A: in the given question we have to find the genral matrix output in terms of a,b,c,d for this first…

Q: (a) Calculate an LU decomposition of -3 6 2 -5

A:

Q: Compute the LU decomposition of matrix A: 9, 4 2 A = 3 -2 -1 %3D 4. 1 633

A:

Q: §8.3, Exercise 5. Suppose the mapping L : R³ → R² is linear and satisfies (:)-(3) ()-6) ()- ) 1 1 2…

A:

Q: 7. Suppose U is an m x n matrix and V is an n x m matrix for which In-VU is invertible. Show that…

A:

Q: Find the matrix associated with the affine transformation Ar +ū for: 1 – 22 - A = -2 12 221 ū =…

A: We are given : Affine transformation: Ax¯+v¯  A=1-22-212221  v¯=-51-3 Hence, we can write the matrix…

Q: Construct a 4×3 matrix A and vectors ~b and ~c in R4 so that ~b is in the range ofthe linear…

A:

Q: (1) Suppose the last column of AB consists of all O's but B itself has no column of zeros. Are the…

A: as you are asking multiple questions I have solved first one , please repost with the remaining…

Q: 2 x + y + z = 2 −3x+3y−3z= 9 −x +7y +3z = −11 Compose the augmented matrix corresponding to this…

A:

Q: 18. Let A be a 3 x 5 matrix with 2 pivots. What is the dimension of Nul(A)?

A:

Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: 6. To identify 3 x 3 matrix Abr fis positive definite if and only if cfr r> 0, r²- ab >0 and 4>0. O…

A:

Q: 8.) Find the LU-factorization of the following matrix 1 2 2 2 3. 1.

A:

Q: 9. Find the QR decomposition of matrix 3 1 -2 A = 1 1 1 -1 2 4 where diagonal elements in R are…

A: Given: A=31-2111-124 We knows that A=QR Where Q is orthogonal matrix and R is upper triangular…

Q: 1. Suppose that (2, 1, 4, 7) and (3, 2, 1, –1) are solutions to a homogeneous linear system, whose…

A: Suppose the given system of linear homogeneous equations can be given as  a11x1+…

Q: Determine the standard matrix of a reflection in R² in the line 3x1 + 4x2 = 0. %3|

A:

Q: Determine the Lower-Upper Decomposition of the matrix A: 3 7 -2 A = 5 1 4 a, represents ith row and…

A:

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: Determine the standard matrix of a reflection in R2 in the line -x1 + 2x2 = 0.

A: Given line is -x1+2x2=0

Q: 3. Find LDU decomposition of the matrix [1 1 1] A = 2 4 3 3 7 6 (а) L 3D (b) D =, (c) U =,

A: Given: A=111243376To find: (a) L=?  (b) D=?   (c)  U=?

Q: Compute the LU factorization of the following matrix. 1 -1 2 -7 A = 2 -5 1 -2 2 -1 6 -21

A: