7. Consider the matrix ´1 1 1 0 0 1 1 1 1 0 1 0 with entries from Z2. Which of the following is row equivalent to M and in reduced row M = echelon form? 1 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 (b)|0 1 0 0 0 0 1 1 0 1 0 1 (a) 0 0 1 1 1 0 0 0 0 1 0 1 (c) 0 0 1 0 1 0 10 0 1 0 0 (d) 0 0 1 1 (e) 0 0 0 1

Q: Consider the 6 × 8 matrix 3 0 0 0 0 1 2 1 0 0 0 0 1 0 0 -3 4 -7 -9 A = 0 0 0 0 0 0 0 0 0 1 8 1 and…

A: The main objective is to answer the sub parts by using given matrix which is in reduced row echelon…

Q: 4 8 12 Transform the matrix into the reduced row echelon form. 2 4 1 1 2 0 0 0 1 Ob. 10 2 0 1 4 O c.…

A:

Q: 1 Suppose that a 3 x 3 matrix A has det A = 1 and that its cofactor matrix is C = 1 2 |-7 4 2 Find…

A: Formula: Let A be a n×n matrix with non zero determinant then, A-1=1det ACT where C is the cofactor…

Q: 3. Consider the matrix 1 2 h 1 M = 13h2 2383 Determine the value(s) of h such that the matrix is the…

A: To Determine: consider the matrix  and determine the value of h such that the matrix is the…

Q: 6. If A is an nxn matrix whose LU decomposition is PA = LU, , prove that det(A) = (-1)' u₁₁ U 22.²…

A:

Q: 1) Consider the following system. 4x1 + x2x3 + x4 x₁ + 4x2x3 x4 -x1 - x2 + 5x3 + x4 X1 X2 + x3 + 3x4…

A: Solving system of linear equations by Jacobi method Let x1=x,x2=y,x3=z,x4=w x(2) means upto second…

Q: 1) Consider the following system. 4x1 + x2 – x3+ x4 -2 x1+4x2 – X3 – X4 -1 -x1 – x2 + 5x3 + x4 %3D…

A:

Q: (1 0 1 0 0 1 1 0 0 0 0 1 1 (0 0 0 0 0 A is a 4 x 5 matrix with reduced echelon form If the -000-…

A: We have to solve given problem:

Q: Given the linear system Ax = b 1 3 -1 -1 -2 5 | 1.5 6.5 7.5 10.5 1 0 -1 1 [x1] 0][1 0|o ,and A LU…

A: 13-12-1-250.251.56.57.510.5-2-7.5-3-3.375x1x2x3x4=b1b2b3b4 Here…

Q: 1 0 0 0 1 0 9. Suppose M Which matrix is M1? %3D 0 3 1 1 00 1 3 0 0 1 0. -3 0. 0. 1 O (1 0 0 0 1 0.…

A: Finding inverse of M

Q: 2. Convert the following rref matrix equation to parameterized solution form. х1 0 0 1 0 0 o 2 0 0 0…

A:

Q: s elect the matrix correspon ding to the form 2 Q(X,, Xz, Xx, Xu ) = - 2x²+ 5 x² - 7× 3 -4 Xú - -4…

A: We have to solve given problem: Concept:

Q: Consider the following augmented matrix of an SLE in 3 variables. а 0ь 2 а 4 4 0а 2 Ь a Determine…

A:

Q: Consider the LP problem: Maximize 3xı + 2x2 subject to: x1 – x2 + 2x3 9 3x1 + x2 – x3 0 Find the…

A: Given LP problem is, x1-x2+2x3≤82x1+x2-x3≥6x1+3x2≥93x1+x2-x3≤10x1,x2,x3≥0 The canonical form of LP…

Q: 6. If A is an nxn matrix whose LU decomposition is PA=LU, prove that det(A)=(-1)' u₁22... Un where r…

A: Given: A is an n×nmatrix, whose LU decomposition is PA=LU.   To show: detA=-1ru11u22...unn, where r…

Q: Use the results of LU decomposition 1 -3 -1 A=LU=|3/2 li/2 1 0||0 1/2 -1/2 1] Lo 1 1 to solve Ax=b,…

A: To solve the equation Ax=b using LU decomposition, given that A=LU=100321012112-3-1012-12001 and…

Q: 3 1 2 Compute the adjoint matrix of A = 3 2 2 1 2 3 Select one: 1 4 а. -7 8 4 -5 3 1 -2 O b. -7 7 4…

A:

Q: 10. Which matrix below is NOT in row echelon form? (1 0 4 4 1 06 0 (A) 0 1 00 0 0 1 0 1 03 4 (C) 0 0…

A: We know that in row echelon form the leading entry of each row is one, but here in B) the leading…

Q: Given that A- -3 -1 -5 2 has the form A = PCP-¹. O P= O 2 -1 1 0 2 and P= O and C= Find an…

A:

Q: If you multiply this elementary matrix: [1 0 0 0] 0 1 0 0 0 0 1 0 E 0 0 0 2 by A to form EA, it has…

A:

Q: The consumption matrix C for the U.S economy in 1972 has the property that every entry in the matrix…

A: Given

Q: 1 4 What is a, if A = is a singular matrix ? %3D 2 a

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: Which of the following 3 x 3 matrices are in row-echelon form? Note: Mark all of your c 1 -7 -8 1 1…

A: The matrix is said to be in row echelon form if: The first non-zero element in each row, called the…

Q: 2. Consider the 6 x 8 matrix [1 30 0 0 0 10 -3 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 5 6. 4. 0 -7 8 -9 A…

A: The dimension of ColA is the number of pivot columms in the corresponding echelon form of A. If A is…

Q: 4) The matrices à = T AT-1 and B=TB is given by 1 1 0 à = -1 1 B : 1 1 1 -2 1 2. 1 1 1 -1 0 1 -2 0 0…

A: Option C is true.

Q: ریاضيات هندسية )1( نظري 3 1 Compute the adjoint matrix of A: 3 2 2 1 2 3 Select one: 4 a. -7 0. 4 -5…

A:

Q: 14. Among the following reduced augmented matrices. Which corresponding system of equations has NO…

A: Given the augmented matrices we write the corresponding system of equations in the variables x,y,z

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

A:

Q: (1 4 6 8 0 2 3 4 0 0 3 8 \0 0 0 4 Is the matrix A = singular? Why? Find A- if it exists.

A:

Q: 7. If a n x n matrix B is obtained from A, using only m number of row interchanges, then det A det B…

A:

Q: [1 Let A = 2 and V = |1]. What is the sum of the entries of the B = %3D 14 5 1 matrix VT (AT — (А -…

A: We have to find sum of entries of given expression.

Q: 2 The matrix is defined as A=( ) has characteristic equation of 12 + DA+ 3, so the value of D…

A: Value of the coefficient of lyambda

Q: if the column sums of a matrix C are all strictly less than 1, then the inverse of the matrix I-C…

A: Assume that the column sum of the matrix C is strictly less than 1. Then for sufficiently large m,…

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: Find the dimension of the null space of the given matrix A. 1. -1 4 A = 2 3 -2 1 2 -2

A:

Q: Consider the matrices 2 1 4 0 13 1 2 -1 0 3 -6 1 |-1 2 -7 1 4 1 17 -1 7 [1 0 3 7 0 8 25 -3 -19 1 -2…

A: Since you have Posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: A manufacturer produces three products x, y, z which he sells in two markets.Annual sales are…

A: The matrix for the product x, y, z per market be denoted by matrix A:

Q: 2) Consider the matrices A = 1 D = [ ] B = K1 = 6 1, K2 = L10 2 [5 l10 2. Solve AX + BY = K1 CX + DY…

A:

Q: Consider the matrix 1 –1 A = 0 -1 1 Compute ||A||2 using the SVD of A.

A: We are given  Hence, we have AAT=211110101 Next we need to find the determinant of AAT-λI Hence we…

Q: Suppose that the augmented matrix corresponding to some linear system Ax = b reduces to the…

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: 8. Suppose that the augmented matrix corresponding to some linear system Ax = b reduces to the…

A: Linear algebra

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

A: We shall solve first question only as you have asked more than one Que of same type. For others…

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: 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: 1 0 0 -1 -2 Ais a 3 x 5 matrix. If AC = 0 1 0 3 4 then the 1 -5 6 size of C is

A: Given : A is a 3 x  5 matrix From the given matrix AC AC is a 3 x 5 matrix We know that , to…

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…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.