Assume that the matrix A is row equivalent to B. Find a basis for the row space of the matrix A. 1 -4 1 4 -5 4 -4 A В %3D 1 -5 -3 -3 -1 -4 1 3 -4 1 -2 3 4 -6 -8 -19 25 {(1, 3, -4, 0, 1), (2, 4, -5, 4), -4, (1, -5, 0, -3, 2), (-3, -1, 8, 3, -4)} О {(1, 3, -4, 0, 1), (0, -2, 3, 4, -6), (0, 0, -8, -19, 25)} {(1, 3, -4, 0, 1), (0, -2, 3, 4, -6), (О, 0, -8, -19, 25), (0, 0, 0, 0, 0)} O {(1, 0, 0, 0), (3, -2, 0, 0), (-4, 3, -8, 0)} 3. 21 II

Q: Consider the following matrix A and its reduced row-echelon form: -3-3 3 3 -9- 1 10-1 0 2 0 0 1 0 1…

A: From rref (A): The basis for row space (A):  The non zero rows of row reduced matrix is,…

Q: The row echelon form of matrix A is given by: [1 2 1-5 31 0. 0 1 3. 4 Lo 0. Then a basis for the row…

A: answer is option C.)  {(1,2,1,-5,3); (0,0,1,3,4)}   explanation is given in below step.

Q: Consider the following matrix A and its reduced row-echelon form: 8 3 4 3 2 0 4 A = 2 6 3…

A:

Q: Given that the matrix A is row equivalent to U: 2 3 4 -2 5 4 05 -1 0 0 0 0 -4 5 -3 A = U 011 4 -4 1…

A: U=-25405-1004000 here we have one pivot entry at all 3 columns so the reduced row echelon form is…

Q: Consider the 6 × 8 matrix 3 0 0 0 0 1 2 1 0 0 0 0 1 0 0 -3 4 -7 -9 A = 0 0 0 0 0 0 0 0 0 1 8 1 and…

A: The main objective is to answer the sub parts by using given matrix which is in reduced row echelon…

Q: Do the columns of the matrix span R³? Select an Answer v 1. 6 6 -1 A 9 8 -5 5 5 0 Select an Answer v…

A: NOTE: Refresh your page if you can't see any equations. . here we have 3 pivot position The…

Q: Given that the two matrices below are row equivalent, find the following: (a) the rank and nullity…

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Q: 9. Assume that matrix A is row equivalent to matrix B, and -1 B = 0 -2 1 -4 A 2 -4 1 -6 5 -6 10 7…

A: Row space of the matrix A is the space of vectors which is generated by the linear combination of…

Q: Find the LU factorization of 3 -1 1 A -3 -6 12 8 20 vrite A = LU where L is a lower triangular…

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Q: 4 1 2 5 1 3 - 7 2. 6 14 16 11 1

A: The matrix A can be written as the product of a lower triangular and upper triangular matrix . The…

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: determine whether the given matrix A is diagonalizable. Where possible, find a matrix S such that…

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Q: Consider the diagonalization of matrix A. 15 A = -8 = SAS-1 1 -2 -1 0 -3 2 24 -13 2 -3 0 3 -2 1 Use…

A: To find A^n

Q: 1 3 1 6 -3 0 -18 4 12

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Q: Thank you!!!

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Q: 6. (a) Find the matrix A so that AB=C, where C1 C2 C3 b, b, bz 2 B= b, b2 b3 & C= C1 C2 C3) а, а аз…

A: AB=C

Q: determine whether the given matrix A is diagonalizable. Where possible, find a matrix S such that…

A: Consider the given matrix, Find the eigenvalues of matrix A. λ1=4,  λ2= i, λ3 = -i The eigenvector…

Q: Find the matrix A given that 1 2 (I +2A)-1 4 5. O a. 4/13] 1 -2/13 13 O b. [-9/13 1/13 2/13 -6/13…

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Q: Given that the two matrices below are row equivalent, find the following: (a) the rank and nullity…

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Q: Given that the two matrices below are row equivalent, find the following: (a) the rank and nullity…

A: First we have to find rank and nullity of matrix A, with the help of equivalent Matrix-

Q: Given that the matrix A is row equivalent to U: -2 5 05 -1 0 0 0 0 2 3 4 4 -4 5 -3 A = U = 011 4 -4…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Which matrix in the follows is in echelon form ? 1 2 01 [1 0 1 0 [2 0 2 01 0. A= 00 1 2 0. 1 0 0 0 1…

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Q: Given matrix A and its row echelon form, E as below: 2 0 2 4] - 3 2 -1 0 [i 0 1 2] E = 0 1 1 3 |0 0…

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: (a) If the columns of annxn matrix A are linearly independent as vectors in R", what is the rank of…

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Q: Find an LU-factorization of the matrix : 4 1 2 5 1 2. 3 - 7 6 14 16 11 1

A: Recall: LU factorization by using Gaussian Elimination method

Q: Determine whether the given matrix A is diagonalizable. If so, find the matrix P that diagonalizes A…

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Q: TRUE/FALSE An n × n matrix A is nonsingular if and only if the reduced row echelon form of A is I…

A: To find: TRUE/FALSE Statement: An n × n matrix A is nonsingular if and only if the reduced row…

Q: 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…

A: (a) It is required to find an echelon form of matrix using row operations. The given matrix is…

Q: -3] Let A be a 4 x 4 diagonalizable matrix, P = |–1 1 1 0 2 1 [1 01 P-1 D = |0 Lo 2 1 3 If P-1 A P =…

A: Given A be a 4×4 diagonalizable matrix. And given matrix is P=00−3−110102, D=100020002 and…

Q: Find a basis for the row space of the matrix 2 4 -5 2 3 A = 6 -8 3 -5 -3 -6 -7 -3 -10)

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Q: Multiply matrix A with matrix B as BA if it is given that: 1 2 -1y 2 2 1 -2 2 -1 and B =| A = 3 1 -1…

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Q: The row echelon form of matrix A is given by: 1 -5 31 0 1 Lo o o 0 [1 3 4 Then a basis for the row…

A: The given problem is to find the row space of the matrix A for the given reduced row echelon form of…

Q: A square matrix is half-magic if the sum of the numbers in each row and column is the same. Find a…

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Q: Given the reduced row echelon matrix A below, identify the rows of A that form a basis for row(A).…

A: Just observe where the pivots are and corresponding rows containing pivots do form basis of row(A).

Q: Given the reduced row echelon matrix A below, identify the rows of A that form a basis for row(A).…

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Q: Consider the matrix 1 -1 3 A = -1 2 -1 Express A in the form A EFGHR, where E, F, G and H are…

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Q: A matrix A and its RREF, R, are shown, below. -2 -14 -1 -5 -6 1 7 0 0 3 | | 0 0 R = 0 0 0 1 35 1 15…

A: The space spanned by rows of A is called row space of a matrix and denoted by row(A) The space…

Q: 4 Find a basis of the row space of the matrix 1 -2 -3 1 1 -3 -3 1 3 A = -3 4 3 -2 6 6 -2 -6

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Q: The row echelon form of matrix A is given by: 2 3 4 [1 0 0 1 2 Lo 0 0 0 Then a basis for the…

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Q: Perform the elementary row operation on the given matrix. -5R, +R,-R, [1 16 5 3] 7 18 5 12 9 13…

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Q: The row echelon form of matrix A is given by: [1 -2 1 -5 -3] 1 4 Lo Then a basis for the row space…

A: The nonzero rows of a matrix in reduced row echelon form are clearly independent and therefore will…

Q: Find the LU factorization of -1 -3 -3 -5 13 -20 27 A = -4 10 -22 25 3 5 4 -6 That is, write A = LU…

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Q: The row echelon form of matrix A is given by: 2 3 4 0 0 1 2 Lo o 0 0 Then a basis for the Nullspace…

A: Given matrix is, The row echelon matrix is,

Q: vector form, where A is row equivalent to the given matrix. 3 -3 7 1 -2 -9 5 1-4 5 0 1 2 -6 7. 9. [6…

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

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Q: Find a basis for the row space and the rank of the matrix. 5.6 10 2 1-3 85-7

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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.