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(1) A is a 3 x 7 matrix, in reduced echelon form, such that the general solution of the equation ...
3 3 -16 -2 -5 12 4 1-12 Find the reduced row echelon form of the...
3 3 -16 -2 -5 12 4 1-12 Find the reduced row echelon form of the matrix B 0 0 0 0 0 0 -16 12 -5 1, and v3 = 1-12 Let Vi 4 17 5 Decide whether the following statements are true or false. 2 The vectors vi, V2, and v span R. The vectors vi , V2 , and V3 are linearly independent. 3 3-16 В 1-2-5 4 -1 -12 Find the reduced row echelon form of...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set o...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
Question 3 please answer clearly. A matrix A and its reduced row echelon form are given...
Question 3
please answer clearly.
A matrix A and its reduced row echelon form are given as follows: [ 2 1 3 41 | 1 2 0 2 A= 3 21 12 | 3 -1 7 9 18 7 9 -4 and rref(A) = [ 1 0 201 0 1 -1 0 0 0 0 1 0 0 0 0 | 0 0 0 0 Use this information to answer the following questions. (a) Is the column vector u= in...
1 The row-echelon reduced form of the matrix -22 3 1 3 2 0 2 0...
1 The row-echelon reduced form of the matrix -22 3 1 3 2 0 2 0 0 -1 -1 0 1 -3 -2 2 is given by 10 0 10 2 R 0 10 0 1/2 -1/2 0 0 1 7 0 -5 Answer the following questions about A: Choose The nullity of A is: 3 Choo Let T be the linear transformation T:R → R given by T(x) = Ax. The number d is: Cha The number of free...
4. Consider the matrix 0- 3 1 -2 1 4 (a) Use Matlab to determine the reduced row echelon form of A (b) If v, V2, vs, v4...
4. Consider the matrix 0- 3 1 -2 1 4 (a) Use Matlab to determine the reduced row echelon form of A (b) If v, V2, vs, v4 are the column vectors of the matrix A, use your result from (a) to obtain a basis for the subspace of W-linsv1, V2, V3, V4. Write the basis in the box below
4. Consider the matrix 0- 3 1 -2 1 4 (a) Use Matlab to determine the reduced row echelon form...
5. Let B be the following matrix in reduced row-echelon form: 1 B= 1 -1 0-1...
5. Let B be the following matrix in reduced row-echelon form: 1 B= 1 -1 0-1 0 0 2 0 0 0 0 0 0 0 0 (a) (3 pts) Let C be a matrix with rref(C) = B. Find a basis of ker(C). (b) (3 pts) Find two matrices A1 and A2 so that rref(A1) = rref(A2) im(A) # im(A2). B, and 1 (c) (5 pts) Find the matrix A with the following properties: rref(A) = B, is an...
And its row echelon form (verify ) is given by 1-3 4-2 5 0 01 3- what is the nullity of A without...
Need answer 11~13，as detailed as possible please
and its row echelon form (verify ) is given by 1-3 4-2 5 0 01 3- what is the nullity of A without solving null space? Let p 3+2r+. Find (p)s, the corrdinates of p relative to S. Find the transition matrix P such that [tle = Plula.. Given lula, = (2,3, 1) what is lul? Determine the bases for row space and column space and the rank of the matrix A 11....
Please highlight answers and answer all questions in each question The reduced row echelon form of...
Please highlight answers and answer all questions in each
question
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x and y as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution 10 -5 0 1 8 What equation does the first row represent? x= -5 (Type an equation.) What equation does the second row represent? y =...
Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row...
Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row equivalent to the augmented matrix c) Find the general solution of the system d) Write the homogeneous system of equations associated with the above (nonhomogeneous) system and find its general solution.
Given the following system of linear equations 1. 2xi + 4x2...
13. Let W = {ī E R4 : Ai = 0} for some constant matrix A....
13. Let W = {ī E R4 : Ai = 0} for some constant matrix A. Suppose all solutions are 1 ES1 lo 1 +r , where t,s,r can be any real numbers. Let S = 0 1 'lo (a) (3 pts) What must the dimensions of the matrix A be? Justify briefly. (b) (8 pts) Show directly from the definition that S is a linearly independent set. (c) (6 pts) Without doing any further) computations, explain why S is...
3 3 -16 -2 -5 12 4 1-12 Find the reduced row echelon form of the matrix B 0 0 0 0 0 0 -16 12 -5 1, and v3 = 1-12 Let Vi 4 17 5 Decide whether the following statements are true or false. 2 The vectors vi, V2, and v span R. The vectors vi , V2 , and V3 are linearly independent. 3 3-16 В 1-2-5 4 -1 -12 Find the reduced row echelon form of...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
Question 3
please answer clearly.
A matrix A and its reduced row echelon form are given as follows: [ 2 1 3 41 | 1 2 0 2 A= 3 21 12 | 3 -1 7 9 18 7 9 -4 and rref(A) = [ 1 0 201 0 1 -1 0 0 0 0 1 0 0 0 0 | 0 0 0 0 Use this information to answer the following questions. (a) Is the column vector u= in...
1 The row-echelon reduced form of the matrix -22 3 1 3 2 0 2 0 0 -1 -1 0 1 -3 -2 2 is given by 10 0 10 2 R 0 10 0 1/2 -1/2 0 0 1 7 0 -5 Answer the following questions about A: Choose The nullity of A is: 3 Choo Let T be the linear transformation T:R → R given by T(x) = Ax. The number d is: Cha The number of free...
4. Consider the matrix 0- 3 1 -2 1 4 (a) Use Matlab to determine the reduced row echelon form of A (b) If v, V2, vs, v4 are the column vectors of the matrix A, use your result from (a) to obtain a basis for the subspace of W-linsv1, V2, V3, V4. Write the basis in the box below
4. Consider the matrix 0- 3 1 -2 1 4 (a) Use Matlab to determine the reduced row echelon form...
5. Let B be the following matrix in reduced row-echelon form: 1 B= 1 -1 0-1 0 0 2 0 0 0 0 0 0 0 0 (a) (3 pts) Let C be a matrix with rref(C) = B. Find a basis of ker(C). (b) (3 pts) Find two matrices A1 and A2 so that rref(A1) = rref(A2) im(A) # im(A2). B, and 1 (c) (5 pts) Find the matrix A with the following properties: rref(A) = B, is an...
Need answer 11~13，as detailed as possible please
and its row echelon form (verify ) is given by 1-3 4-2 5 0 01 3- what is the nullity of A without solving null space? Let p 3+2r+. Find (p)s, the corrdinates of p relative to S. Find the transition matrix P such that [tle = Plula.. Given lula, = (2,3, 1) what is lul? Determine the bases for row space and column space and the rank of the matrix A 11....
Please highlight answers and answer all questions in each
question
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x and y as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution 10 -5 0 1 8 What equation does the first row represent? x= -5 (Type an equation.) What equation does the second row represent? y =...
Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row equivalent to the augmented matrix c) Find the general solution of the system d) Write the homogeneous system of equations associated with the above (nonhomogeneous) system and find its general solution.
Given the following system of linear equations 1. 2xi + 4x2...
13. Let W = {ī E R4 : Ai = 0} for some constant matrix A. Suppose all solutions are 1 ES1 lo 1 +r , where t,s,r can be any real numbers. Let S = 0 1 'lo (a) (3 pts) What must the dimensions of the matrix A be? Justify briefly. (b) (8 pts) Show directly from the definition that S is a linearly independent set. (c) (6 pts) Without doing any further) computations, explain why S is...
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