Consider a matrix A, and let B= rref(A). %3D a. Is ker(A) necessarily equal to ker(B)? Explain. b. Is im(A) necessarily equal to im(B)? Explain.

Q: Due to what property, applied to the matrices below, do we know that A + (−A) = O?

A: A+-A=O

Q: For the matrix A = 4    5    8                               2     3    6…

A:

Q: What do we mean by the transpose of a matrix?

A: Matrix is a set of number which are arranged in form of rows and columns. They have elements in them…

Q: For matrix A, (A^3) = 1, A^(-1) is equals to: * A^2

A:

Q: Consider the following matrix A, where -2 4 -2 -4 A = 2 -6 -3 1 -3 8. 2 -3

A:

Q: Which of the following is the order of its transpose in a matrix of the form ? * * O A) 6x2 О В) Зx3…

A:

Q: Given matrix A, A + −A = _____?

A: To Determine: find A+-A Given: we have a matrix A Explanation: let us consider a matrix A=1245 then…

Q: find an LU factorization of the given matrix.

A:

Q: Given a 1000-by-1000 matrix Y, let - (6 ?). Y A = What

A: Given that A=IY0I By the GMRES, By the conjugate method, the residues form an orthogonal basis for…

Q: Disprove that the rank of a matrix is equal to the number of nonzero rows.

A:

Q: What is the rank of the matrix?

A: Given,

Q: Consider the matrix. -6 3 C = -5 4 What is the value of C|? |C| =

A: Given matrix : C=-63-54 We have to find the determinant of C i.e. |C|

Q: If A = [1 2 3], which type of the given matrix A ?

A: Given Matrix A=[1  2  3 ]1×3  Here number of row=1  Number of columns=3

Q: Determine the matrix if it is a linear combination of O A.c = 5; d = 8 O B. c = -5;d =8 O C.c = 8; d…

A: 12cd = a1-1-1-1 +b3159 + m41611 + n-1234 Therefore, we get a+3b+4m-n = 1…

Q: Q1: Given that A = [3 -3 -5] and B = 5,what is the matrix A- BT?

A:

Q: An identity matrix is represented by... . а. Нн-1 O b. HH-H C. H-H

A: Given

Q: In plain-speak, what is a matrix?

A: Definition of matrix helps to get the answer to the problem. There is a wide application of matrix…

Q: Let A be an mtimes×n matrix and let B be an ntimes×p matrix. If the first row of A consists only of​…

A:

Q: What is the rank of the matrix?

A:

Q: Illustrate the Skew-symmetric matrix ?

A:

Q: If A is a skew symmetric matrix, what type of matrix is A T ? Justify your answer.

A: Given: A is a skew-symmetric matrix.

Q: For Exercise, use the following gray scale. 2 3 5 6. light gray white medium gray medium medium dark…

A: (a)

Q: The matrix given is A=[a1,a2,a3] | 3 1 -1||-2 0 -2||-3 -3 1|   Find A5

A:

Q: Find an LU factorization of the matrix A (with L unit lower triangular). -3 3 A = 3 - 3 6 15 18 L =…

A: Topic = Matrix

Q: What is the minor of the element 5 in the matrix below? C 154 2 36 794

A:

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 4 8 A = 16 30

A:

Q: Given the matrix 1

A:

Q: An identity matrix is represented by.... а. Нн-1 b. HH-1H O c. H-1H

A: Given problem:-

Q: [2 Given the matrix

A: As per the instructions, we will be solving only the first question. We will be solving 2131xy=21.…

Q: Consider the matrix A = Calculate a22 = 8 5 d n -( :-(29 766 b f 468 h с Calculate 932 = a e

A: It is provided that: A=852766468·dngbfahce. We need to calculate a22, a32.

Q: 3. PD. For these values, determine the Cholesky factorization of the matrix A.

A:

Q: What is the reduced row echelon form of matrix A? A = 어405 ON 11 O- O N

A:

Q: If A is a skew symmetric matrix, what type of matrix is AT ? Justify your answer.

A: If A is a skew symmetric matrix, then our aim is to tell the type of AT matrix?

Q: a small barangay, there were a farmer, a baker, and a grocer and has the input-output matrix D and…

A: follow next step

Q: Given that A is a 4 × 2 matrix and B is a 2 × 1 matrix, a. Is AB defined? If so, what is the order…

A: a) A is a 4 × 2 matrix and B is a 2 × 1 matrix Since number of coulmns of A=number of rows of BSo AB…

Q: An identity matrix is represented by... О а. Нн-1 O b. H-1H О с. Нн-1н

A: If we multiply a matrix by its inverse we get the identity matrix.

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 6 4 A= 12 5

A:

Q: Find all values of a such that A3 = 2A, where   (see image of matrix)

A: Consider the given matrix,

Q: Find the values of a, b, c, and d in the matrix equation below. [:] 10 -5 -8 -1 b. + 2 -8 -10 7 a =…

A: We will find the value of a,b,c and d of the given matrix in the following step.

Q: Find the value of z in the equation matrix. 4 + 2 a. 1/2 C.-1/2 b. 1/4 d.-1/4

A: We have to solve the problem

Q: For which value of k will the columns of the following matrix be linearly dependent?

A: objective is to find the value of k.

Q: -2 ky For the matrix A 2 if JA| = 0, what is the value of k? 3/

A: C.   -3 D.    Both B and C

Q: What is a column matrix?

A: Definition of column matrix – A vector which is represented with a list of number is called a column…

Q: * For the matrix shown, calculate 3 2 A , where A = -1 4 1 1 1 6 3

A:

Q: Consider the matrix. -3 5 C = %3D -2 4 What is the value of ? |C|- %3D

A:

Q: If A is a 4 x 15 matrix, what is the largest rank possible? Your Answer:

A: If A is a ,4 * 15 matrix   Then largest possible rank of A =, min { 4 , 15 }

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.