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: 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: Find a basis for the mullspace of the following matrix: [1 0 - 1 -5 4 3 -2 1

A:

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

A:

Q: We call a matrix B a square root of A if B2 = A.

A:

Q: Is the following matrix diagonalizable?

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

A: Initial matrix is, -11145033901010

Q: Find the row reduced echelon  matrix R and invertible matrix P such : R = PA             -1     1…

A: The given matrix is: A=-11-10-34114-6-4-2310-14. To find row reduced echelon form of given matrix,…

Q: Does the matrix 1 −1 -2 1 0 -1 have an LU factorization? If so, compute it. If not, explain why not.…

A: We have given a matrix, B=21-1-4-2130-1. A square matrix is said to have an LU factorization if it…

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

A:

Q: [2 Given that; a=1, b=2, c=0, d=1 Explain why the matrix a b c d is not diagonalisable.

A: Here the given matrix Let x be tha eigen value of A matrix Then

Q: Let B = and C = {c1,c2} be bases for R?. Find the change-of-coordinates matrix from B to C and the…

A: The bases B and C for ℝ2 is given as follows: B=b1, b2=-12, 1-1C=c1, c2=12, 11 We are asked to find…

Q: Given a matrix A = for what conditions on a, b, c, and d will the matrix not have an inverse?

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: Consider the following augmented matrix: 0 0 2 0 3 | -3 5 1 00 1 22 -1 1 a. Is the matrix in…

A: NOTE: Refresh your page if you can't see any equations. . the given augmented matrix is  as we can…

Q: Express the column matrix b as a linear combination of the columns of A. (Use A₁, A2, and A3…

A: The given matrix and a vector, and .The objective is to write the vector  as a linear combination of…

Q: Build a Mumber line 2| 4 ||-8|| O -2|-6|-10 || 6 8 ||-4|| 10

A: The number line are as follows

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.