Evaluate: Use 3 decimal places [1 9' 10 b =|0 1 4 o] 4 -3 A = | 8 -4 12 -8] Find the value of the variables of the linear equation using Doliitle LU method. Write the matrix of A = [L\U].

Q: Complete the matrix A so that it is skew-Hermitian. i 2—6і - A = 1 9i Y = = 2

A: Given the matrix, A=0i2-6ix01yz9i The matrix A is said to be skew-Hermitian matrix if, A*=-A Where…

Q: Let x and y be linearly independent vectors in Rnand let S = Span(x, y).We can use x and y to…

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Q: * Find the values for h for which the vectors are linearly dependent: 7

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Q: Give a matrix representation of the quadratic form f(x, y, z) = 4x 2 + 9y2+ 16z 2 − 2xy + 4xz − 6yz…

A: Given: f(x,y,z)=4x2+9y2+16z2-2xy+4xz-6yz             We have to find a matrix representation of the…

Q: Use software of your choice to compute T2, T, T®,T16 – this is most easily accomplished by squaring…

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Q: In Exercise, find the singular values of the given matrix.

A: A singular value decomposition of is a factorization                             A = U∑V Twhere,…

Q: Determine the values of x, y, z based on the following matrix equation by using LU decomposition…

A: Given matrix equation  1-312-88-63-15xyz=4-29      ......1 This is of the form Ax=b. A can be…

Q: Determine all values of the parameters x and y such that the vector 1 s in the range of the above…

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Q: Find the inverge of the 2x2 matrix Cos t Sin t - Sine Cose

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Q: d. Form [T2] and [T1] and compute the matrix products [T2][T1] and [7T1][T2]. Verify that they equal…

A: The solution is given as

Q: Use the first-order approximation to find the approximate inverse of the matrix [1.1 0.1 0] C = 0…

A: Given matrix 1.10.1001.9-0.10.204

Q: Answer considering the matrix with th e given vectors as its columns

A: Given: The given matrices are, Assume the linear combination as follows,

Q: Find the triangular factorization A = LU for the matrix A = 1  1  6      -1  2  9       1  -2  3…

A: Given       A=116-1291-23

Q: Show that LU decomposition is not possible for the matrix A, where 1 2 3 A 2 4 1 0 2

A: The given matrix is,A=123241-102

Q: Determine the residual and Jacc - bian needed to solve the equation d²u 2u° = 0, - dx? 1 and u(1) 0,…

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Q: Find the standard matrix of the linear operator M: R2 R2 that first reflects every vector about the…

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Q: Rewrite as a matrix-vector product: Зх + 4у — z + w%3D 12 -x + 2y – z +w = 9 2х — Зу + 2z — 4w %3D -…

A: Here we have to rewrite as a matrix-vector product:  3x+4y-z+w=12-x+2y-z+w=92x-3y+2z-4w=-3

Q: 3 2 2 1 a) X1= b) Уi%3D| - 3 y2=| 1 X2= 3 X3= 1 4 y3= 1 3 1 N O

A: X=x1,x2,x3 be set of vectors. Let A=x1,x2,x3 and AT=x1x2x3 G=AAT where G is dram matrix. If G is…

Q: 2. Rearrange the equations to form a strictly diagonally dominant system. Apply two steps of the…

A: The complete solutions are given below

Q: Find the standard matrix of the linear operator M : R → R³ that first rotates all vectors…

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Q: Construct a matrix A E M22(R) so that the solution set of the homogeneous equation Ar = 0 is a line…

A: We know that the homogeneous system of linear equations is written as Ax=0. Here we have to choose…

Q: Let A = (a;;)ij be an m x n matrix of real numbers, and let f : R" -→ Rm be defined by x2 X2 f = A…

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Q: Use the definition of Ax to write the vector equation as a matrix equation. 2 + Z4 + Z3 4 + Z2 19…

A: The given vector equation is, z145+z2-42+z314+z4-32=-219.

Q: condition must a and b satisfy for the matrix to be orthogonal? a – b b+a

A: We find the condition on a and b

Q: Find the matrix A representing the reflection about the line L in R² which consists of all scalar…

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Q: what is the linear combination of  u⃗  and v⃗ ?

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Q: 2rị + 13 T: R' → R?, T 21, 22, 13, L4 ER -12 - 3r4

A: Given  and the standard bases are given by

Q: Solve the following linear system of equations using Cramer's Rule

A: We have to solve the following linear system of equations using Cramer's Rule.

Q: Find the value of h for which the vectors are linearly dependent

A: The given vectors are 1-14 , 3-57 , -15h The vector v3 are linearly dependent if the equation…

Q: Determine whether the span of the column vectors of the given matrix A is equal to R^3. Show your…

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Q: Give the General Solution:  (d/dt)(vector(x)) = matrix(-2,1,0,-2)vector(x)

A: The given system is as follows. ddtX=-210-2X Find the eigenvalues of the coefficient matrix as…

Q: Find the standard matrix of the linear operator M : R R' that first project every vector through…

A: We have to find Standard Matrix of Linear Operator  M : R3 -> R3

Q: Use the definition of Ax to write the vector equation as a matrix equation -2 + Z2 - 5 3 +Z4 2 4 Z1…

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Q: Find the value of h such that the vectors ()()(E) 1 2 h 1 1 are linearly dependent? Show details of…

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Q: Consider the matrix A and the vectors p and q. 1 -3 9. A = -3 0 p= -6 | q = | -9 2 4

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Q: с pose the vector -6 is in the nullspace of the matrix d 6 -4 34 1 -5 23 1 -7 rmine c and d giving…

A: Topic:- application of algebra

Q: SOLVE FOR ORTHOGONALITY AND NORMALIZED CONDITION GIVEN THE 3 X 3 MATRIX. [1.000 1.000 1.000 0.686…

A: Given matrix is 1.0001.0001.0000.686-0.500-2.1860.314-0.5003.186

Q: First change the given pattern into a vector w of zeros and ones by turning each shaded square into…

A: M = 0 will be the right answer.

Q: Express the quadratic form as v Av, where A is a symmetric matrix. x² + 3y² + 5z² - 4xy+3yz + 10xz

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Q: Is Vector Y in the Column space of A? What is the solution set? Write y as an appropriate linear…

A: the vector y is in the column space of A is the system Ax=y is consistent 819-59-13108abc=123…

Q: +0, then the matrix H = I – 2- vv7 is orthogonal and symmetric. Show that if the vector v

A: Given  H=I-2vvTvTv

Q: Show that the condition number of the square matrix, X (generated with X;j = 461-2), grows i+6j–2 as…

A: We will use the conventional definition of condition number of a matrix.

Q: Find the coordinate matrix of x relative to the orthonormal basis B in R". {( 3/10 0, 10 V10 3/10 0,…

A: The solution is given as

Q: Gve an example of a dx2 matrix A and 2-dimensional vectors u and v such that u and v are orthogonal…

A: We have to give an example of a 2×2 matrix.

Q: Given the matrix 2 2 2 3 1 A = 0 2 7 7 Find the |A| by transforming the matrix A to the triangular…

A: Given :A=222023771

Q: Use the definition of Ax to write the vector equation as a matrix equation. 4 - 3 + Z4 4 4 + Z2 + Z3…

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Q: Complete the matrix A so that it is Hermitian. 6 – 3i 1 A = -4 1 2 2 =

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