9 0 3+i 7 4 2- i A= 2+ i 9 3- i

Q: et A be tx8 matrix. Knowing that Nullity (A) = 2. The %3D

A: In the given question, the concept of rank plus nullity theorem is applied. Rank plus Nullity…

Q: What i and j must satisfy if a_ij is on the main diagonal? above the main diagonal? below the main…

A: 1) If aij is on the main diagonal, then i must be equal to j. If aij is above the main diagonal,…

Q: Describe the possible echelon forms of a nonzero 6x 2 matrix. Select all that apply. (Note that…

A: Given, the possible echelon forms of a non-zero 6 x 2 matrix.

Q: True or False: 1. If an n x n matrix AA has all zeros on its main diagonal then det(A)=0. 2. If A…

A:

Q: Determine the dimension of the matrix. 0 7 15 0   −3 0 3 3 −1 1 6 7

A: Explanation of the solution is given below....

Q: aj bị c1 adjA if A = |a2 b2 c2| is a non-singular matrix prove that A: detA аз b3 C3

A: Matrix A is a non-singular matrix. This means; det A ≠ 0    A =a1b1c1a2b2c2a3b3c3adj A…

Q: Diagonalize B, i.e. Find the invertible matrix P and diagonal matrix D satisfying B = PDP¯1. (Note:…

A:

Q: Г1 2 3 4 5 A = 5 0 2 4 6 8 5 5 5 5

A:

Q: 0 5 Let A= 4. diagonalizable matrix( A-XDX), then X and D are: 1 Select one: a. -5 X= -5 0 4 0. b.…

A:

Q: 2. Verify that detAB = det A(det B) for the given matrices %3D 1 -2. 3] [1 1 21 A =-2 3. 1 and B 3.…

A:

Q: 2 The matrix A = can be 1 diagonalized. Select one: O True O False

A:

Q: True/ False (Explain) Q# 45)If A is any invertible matrix, then det(A)=0

A: Given  If A is any invertible matrix, then det(A)=0

Q: In general, matrix multiplication is not commutative (i.e., AB = BA). However, in certain special…

A:

Q: A is a matrix and there's a vector x, and Ax is defined. Can the equation Ax=0 have no solution ?…

A:

Q: 13.) Determine the matrix: s P 6-8 3 ។ -3 the dimension X 10

A:

Q: I. True of False Choose True if the statement is correct, otherwise False. 1. Matrices are often…

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Q: Determine the dimension of the nullspace of the matrix Г1 2 3 M 0 1 0 O 1 O 2 O 3

A:

Q: Determine the Null Space of the (3x3) matrix A for which (2j + i aij if i # j if i = j %3D i+ti

A:

Q: 4. Determine whether the matrix is nonsingular or singular. 6ive reasont -11 0 3 2-2 1 le

A: When the determinant of the matrix is zero,                      Then the matrix is said to be…

Q: Find the innverse of the matrix b: 5 0 6 9 1 2 3 4 9 3 5…

A:

Q: 4) Given the matrix A= (! ), find all matrices B such that AB=BA. Check partic ular matrix B. your…

A:

Q: [2 3 4 3 4 5 6 20. Calculate the rank of the matrix P = 4 5 6. 7 9 10 11 12 'n

A:

Q: 24 Let B be a Sx5 matrix and Ca(): A-1)(X--いメ) Let W represent the solution set to the System. Yu Xu…

A: Given that B is a 5×5 matrix and CAλ=λ-1λ2-λ-6λ2+1 Also given that W is a set of solution to the…

Q: 3. What is the dimension of the vector space consisting of five-by-one column matrices where the…

A: Option B i.e 4

Q: 12 is diagonalizable. The matrix A = %3D 0 1 True False

A: Given that  The matrix  To find the matix is diagonalizable or not

Q: 25. (a) Find all 2 × 2 matrices whose null space is the line Зх — 5у — 0. (b) Describe the null…

A:

Q: 3 6 Let y = [8] Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to…

A:

Q: 1 0 0 3 0 1 0 0 0 0 0 0 0 0 -6 [1 1 -4 8

A: For the solution one needs to convert this augumented matrix in Ax=b form then it is easy to see…

Q: Quèstion 14 Which matrix is singular? 6 -3 21 2 6 3 o( 2 6 2 6 3 1

A: topic - singular matrix a matrix is singular if its determinant is zero

Q: The column space of a matrix is the set of solutions of Ax=b.Mark this statment as True or False.…

A: The column space of a matrix A is the set having all of the linear combinations of columns of matrix…

Q: 1. True or False ? Why? Let A be mxn matrix. If the augmented matrix [A|b] has rank strictly less…

A: Here we give a counterexample of this statement.

Q: ind the null space and the nullity of the matrix A. 1 -3 - 6 4 -2 5 4 2 9. -1 8 2 -6 9. -1 9 7 -1 -…

A:

Q: 3 b Find the value of b that make the matrix A singular. 3 5 b =

A: Note : According To our guidelines we can solve only first question and rest can be reposted.Thank…

Q: Find the null space of matrix A which is 1 3 13] 7 3 8 A =-2 -5 -3 0 3 2 6. 24 3 13 1 2. 6 3.

A:

Q: 22. Find all 3x3 matrices for which the homogeneous system has a solution space as the line x= 2t, y…

A: ANSWER :

Q: What is the null space of this matrix:   A = 3 0 0 2 0 0 1 1 1

A:

Q: Let A be 5x6 matrix. Knowing that Nullity (A) = 2. Then Rank(A) is equal to: * None of these O 2 O 1…

A: We will find the rank of A as following.

Q: 3. (30 points) Diagonalize the matrix A = 5 0 1 -1 05 0 0 0 0 4-3 0 -2 0-3 if possible.

A: 5000050000-30000-3

Q: 2. Find the change of basis matrix from B to B' and the change of basis matrix from B' to B.

A:

Q: There are no two fundamental matrices for the same system (i.e. The fundamental matrix is unique).…

A: " FALSE"  A fundamental matrix has n linearly independent columns, each of them is a solution of the…

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: 22. Find all 3x3 matrices for which the homogeneous system has a solution space as the line x = 2t ,…

A: Answer :

Q: Find the null space of matrix A which is 1 1 3 7 6 3 8 A = -2 -5 -3 0 3 0 2 4 3 5 13 1 3. 3. 2.

A: A null space of matrix A is the space that consists of all the vectors X such that AX=O…

Q: 4. and u = Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u.…

A:

Q: 2 2 1 2 -1 2 is orthogonal. Verify whether the matrix A = 3. -1 2 2

A: Given matrix is, A=132212-12-122

Q: If I is the identity matrix then det(I)=0 Select one: True False

A: If I is identity matrix then det(I) =1

Q: 3. Find LU factorization of the matrix A and show that A = LU. 3 1 3 6 4 8 -10 3 2 5 -4 A = -1 -9 5…

A: method. A= LU L= lower triangular matrix  U= upper triangular matrix  first find the first row of U…

Q: Let a - .- 3 -1 21 A = [ 1.8 = ; -21 -31

A: The Addition or Subtraction of matrices is possible only when matrices are of same order.

Q: Which one is the transpose of matrix below? 2 1 1 A = (aj) 0 2 5 -5 9.

A: Transpose of a matrix is obtained by changing rows to columns and columns to rows. In other words,…

Q: 7: The norm of the matrix A O True O False [3 1 11 3. is equal 4.

A: As per our guidelines we are allowed to answer only one question. Kindly repost the other questions…

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.