® Given 1 is a solution for the matrix equation A8=B. Determine and explan why each statement is True or Falbe (No explanation, zero point) a) A is an invertible matrix. b) B=-A,-2A2-A3, where Ar,A2A3 are columns of A. c) The list (A,Az, As) is lineorly dependent

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…

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A:

Q: The reduced row echelon form of the matrix A is I3 . Describe all possible matrices A.

A: Consider the reduced row echelon form of a matrix A is I3. We need to determine all possible…

Q: 8) Show that the matrix -1 Bz 1-4 4 -3 -2 is idempotent.

A: Given…

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A: We have to find: a. order of matrix b. a32 and a23 when A=ai j And matrix is given as A=4-75-68-1…

Q: Find the basis of row space of the matrix A given in the attached image . Please answer quickly .

A: A=1231337638-2-5-30326024351312R2⇒R2-3R1, R3⇒R3+2R1, R4⇒R4-2R1,…

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A: Solution:-

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Q: Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A.…

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Q: 2.3 Explain how you obtain the matrix N that rotates a point 180° anticlockwise around the point…

A:

Q: 3 4 Let X and Y in the set of 2 × 2 matrices, M22. %3D -11 2 3 Determine whether A = or B are in…

A: Given  X=2-121, Y=34-11 and A=0-1181, B=2312

Q: Explain row vector in a 1 x n matrix?

A: To analyze row vector in a 1 × n matrix.

Q: 2. Consider the 6 x 8 matrix [1 3 0 0 0 0 1 0 2 0 5 -3 0 0 0 A 0 0 1 4 -7 -9 00 0 0 0 0 0 0 0 0 0 0…

A:

Q: Let A be a 3 × 3 matrix with the following property: 2 times the 1st column minus 3 times the 2nd…

A: To find all the nontrivial solutions of Ax = 0. Also to describe the geometry of the solution set.

Q: Consider a 3 x 4 matrix A in reduced row echelon form. What can you say about the image of A?…

A: We have say about the subspace Ab where b from R4

Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

A: We will find out the required value.

Q: b) Determine whether the matrices L- ), M = [ - 3 - 2 2 4 3 ,and N = -2 2 are linearly independent…

A:

Q: (b) Explain why in general, if u = [u uz] is a row of length 2, A = a1,1 a1,2 [@2,1 @2,2] we always…

A: Answer

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A:

Q: What type of matrix is a linear combination of scalar ma- trices? Justify your answer.

A: Consider n scalar matrices with each matrix in k×k order: A1, A2, A3, ⋯, An Also, let b1, b2, b3, ⋯,…

Q: Explain why the row vectors of a 8 × 7 matrix form a linearly dependent set. (Assume all matrix…

A: Consider the given information. The given matrix in the form of 8 *7 matrix, forms a linearly…

Q: 2 -2/2 2/2 , show that A and B satisfy 2 Q#5: If A= and B 2 commutative property with respect matrix…

A: Given  A=2-2222  and  B=222-22. We have to show that  AB=BA.

Q: Give the row operation used between each augmented matrix. Use R1, R2, ... for Row 1, Row 2,..,…

A: In this question, concept of row operation in augmented matrix is used. Augmented Matrix Each row…

Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

A: write v=7,5,-11,14,6 as a linear combination of u1, u2 , u3, u4, u5 where…

Q: Use (ii) of the rank of a matrix by row reduction theorem to find the rank of the given matrix. (?…

A: The given matrix is 7-113.

Q: Explain why the row vectors of a 7 x 2 matrix form a linearly dependent set. (Assume all matrix…

A: Rank of the matrix is at most min(7,2) = 2 dimension of row space = rank of matrix

Q: he matrix is Α = et result hitting · 230 1 -1 3 401 -1 Α Α ΑΑ

A: Topic:- matrix algebra

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

Q: Construct 4x4 matrix A= Lajj whose a entries satisfy Ja;;=2i ij=1, 2, 3,4 %3D

A:

Q: Suppose the third column of B is the sum of the last two columns. What can be said about the third…

A: Answer is mentioned below

Q: Let matrix A be 2 by 2 matrix and 1 A. 4 and 1 4 .2) 2 Then what is A=? ||

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Q: Is it true that Every identity matrix is a diagonal matrix? explain a reason?

A: A square matrix B=[bij] of order n is a diagonal matrix , if all its non-diagonal elements are 0,…

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A: Given: The Matrix is 4 * 3 matrix

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A:

Q: 2. For what value(s) of h will y be in Span{v1, V2, V3} if 17 57 -3 -4 Vị = -1 V2 = -4 %3D V3 = 1…

A: Given vectors are v1=1-1-2, v2=5-4-7 and v3=-310 Also given y=-43h is in span of v1,v2,v3 So ycan be…

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

Q: Give an example of a matrix A and a vector b such that the solution set of Ax = b is a line in R'…

A: System of linear equations

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Q: V. Let A be a 3×3 matrix and let b= 3a, +a, +4a,· Will the system Ax=b be consistent? Explain.

A: Given that A is a 3*3 matrix andet b=3a1+a2+4a3

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

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A: Given row space is, 4,7,5 and 2,3,-5 And the null space is, 2,1,3

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A: Echelon matrices come in two forms: the row echelon form (ref) and the reduced row echelon form…

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A:

Q: 4. Describe all matrices row equivalent to the matrix: [B]

A: Since you have posted a multiple question according to guildlines I will solve first(Q4)   question…

Q: A and B are two sequar upper triangular matrix then ove that the JAB| is equal the product of its…

A: Topic:- matrix algebra

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A:

Q: (6 1) is diagonalizable. Determine whether the matrix A

A: To determine whether the given matrix is diagonal or not, we will use the following theorem: An nxn…

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.