a) Use row ops to find an echelon form of:   A =  1 2 2 -2 2 2 4 1 -2 5 1 2 -1 0 3 b) Use the echelon matrix found above to find a basis for RS(A), NS(A), and CS(A). Give a brief reason for your choice. Without a justification, you might just have a lucky guess and I will not accept this. Your justification can be short and use facts from the text or from the notes that I have provided. c) Show that skew-symmetric 3×3 matrices form as subspace of all 3×3 matrices and find a basis for this subspace.

Q: Let A = 2 1 54 Write 5A. Is det(5A) equal to 5det(A)? 5A= (Type an integer or decimal for each…

A:

Q: Diagonalize the following matrix. 900 19 0 0 0 10 Select the correct choice below and, if necessary,…

A:

Q: Consider the matrices 4 2 1] 5 4 B = 2 2 3 1 A = X = -3 0 1 2 0 8 Which of the following matrix…

A: We have  Matrix multiplication AB defined only if Number of columns of A = Number of rows of B

Q: Given the following matrices below, confirm or deny that (BT AT)-¹ = (A-¹B-¹)". 4 5 2 -8 6 2 3 B = 2…

A: The WOLFRAM MATHEMATICA CODE to perform the required operations is given below. THE CODE A = {{4,…

Q: Find out the pivots of the following matrix and comment whether it is singular or not. 2 0 0 1 10 0…

A:

Q: Q1: For the given matrix A, find (a) The rank of the matrix A, (b) a basis for the row space (c) a…

A:

Q: 1. Find A-¹ using elementary row operation to the augmented matrix. Let A = -2 10 0 0 4 2 -6 -12

A:

Q: Ex. 600. Given the 2x2 Matrix A 1 2 11 3 Determine B=A+A and C=A-A Answers:…

A:

Q: Find a formula in terms of k for the entries of Ak, where A is the diagonalizable matrix below and…

A:

Q: (3) Consider 1 -4 9. -7 1 -1 5 A = -4 1 B = -2 -6 -6 10 7 and assume that the matrix A is row…

A:

Q: compute the indicated matrices A + 2D

A:

Q: Diagonalize the following matrices a) (0 0 1 2 -2 A : 1 1 0 3 b) 3 2 A -2 -2 -2 1 2 2

A: We find the eigenvalues and corresponding eigenvectors of the given matrix to diagonalize it.

Q: Consider the following matrix A and its reduced row-echelon form: 5-6 103 2 12 -3-69 12-15 18 0 1 -3…

A:

Q: 3. Consider the following matrix: A= | 1 0 0 1 1 (a) Construct the QR factorization of A. Write all…

A: Let us solve the given problem in the next steps.

Q: Find a vector that is orthogonal to each of the three vectors below: V1 = 1 V2 = 0 1 0 and V3 = 1 3…

A:

Q: A. For any matrix A, give a simpler name for the matrix (At)t. B. Is it true or false that (2A)t =…

A:

Q: We changed the first nonzero entry beneath the pivot to a zero and found the following augmented…

A: Initial matrix is, -11145033901010

Q: Diagonalize the following matrix. [4] Select the correct choice below and, if necessary, fill in the…

A:

Q: Diagonalize the following matrix: 1 13 5 7 -5 -7 -1 -1 7 90 06 0 00-12 060 − 1 1 − 1| -1 0 1 1 10 1…

A: Given matrix 11357-5-7-1-17

Q: 3. Let [1 2 3 A = |4 5 6 7 8 9 (a) What is Aēj? Present it as a linear combination of the columns of…

A: Given

Q: its) Consider the following matrix A: A = a. Find a basis for the rowspace of A. b. find a basis for…

A: Given matrix A A=1231001712

Q: Find the rank of the following matrices: 1 2 2 3 3 2 1 тank(A)— 2 3 таnk(A)—

A: We use the definition of the rank of a matrix to find the rank of given matrices.

Q: 1 2 C= 1 A = 1 -2 3 D = 1 1 1 -1 1 -1 -9 B = 1 1 1 1 2 -1 -1 4 1 find the matrix 2A – 3B + C. Do…

A: Given A = 11-2110B = 11-1111C = 1232-11D = 1-1-9-141

Q: a. Find a basis for the rowspace of A. b. find a basis for the columnspace of A.

A: Given Matrix A=12310abc12 We are also given a=0, b=1, c=7 Hence matrix A becomes A=1231001712

Q: Consider the matrices A, B, C. 1 4 2 --1 3 3 -1 3 A =|3 0 1 B = C = 2 6 8 0 5 6 -1 5 7 2 a. Find the…

A:

Q: Show that A = P-¹ = 2 -1 -5 2 -2 -2 0 1 -4 and B = 3 6 -8 2 2 -4 , P = 4 6 are similar matrices by…

A: Given: and To show: and  are similar matrices by finding an invertible matrix  satisfying

Q: Given the matrix A = Then A¯¹: = 1 2 4 1 5 Select one: O True False -1-2 1 2 -5

A: Given query is to find statement is true or false.

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.