Homework Answers
Question 3. (20 pts) Let A= -3 9-27 2 -6 4 8 3 -9 -2 2...
Question 3. (20 pts) Let A= -3 9-27 2 -6 4 8 3 -9 -2 2 Find a basis for Col(A) and a basis for Nul(A). Question 4. (15 pts) Let the matrix A be the same as in Question 3. (1). Find the rank of A. (2). Find the dimensions of Nul(A) and Col(A). (3). How do the dimensions of Nul(A) and Col(A) relate to the number of columns of A?
A= 9 2 3 -9 -2 Question 4. (15 pts) Let the matrix A be the...
A= 9 2 3 -9 -2 Question 4. (15 pts) Let the matrix A be the same as in Question 3 (1). Find the rank of A. (2). Find the dimensions of Nul(A) and Col(A). (3). How do the dimensions of Nul(A) and Col(A) relate to the number of columns of A?
6. (15 pts) For the linear system 3x + 2y + 10x = -6 3 +...
6. (15 pts) For the linear system 3x + 2y + 10x = -6 3 + 2z = y+2z = 3 3+ 4y + 10% = 8 a) Use your calculator to place the augmented matrix in RREF and write it here. 3 2 10 -6 i 470 - 4 3 8 b) Find the general solution to the linear system, written as either the vector equation of a line or the vector equation of a plane.
Problem 1 Let A= 3 2 13 1 5 7 11 8 -3 9 10 -6...
Problem 1 Let A= 3 2 13 1 5 7 11 8 -3 9 10 -6 -4 12 8 a) [4 pts) Find a basis for N(A) in rational format. b) (3 pts) Find a particular solution to the matrix equation A*x= 5 -2 14 c) [3 pts] Use your answers in a), b) and the Superposition Principle to express the general solution in vector form to the matrix equation in b).
Question 3. (20 pts) Let A= -3 9-27 2 -6 48 3 -9 -2 2 Question...
Question 3. (20 pts) Let A= -3 9-27 2 -6 48 3 -9 -2 2 Question 4. (15 pts) Let the matrix A be the same as in Question 3 (1). Find the rank of A (2). Find the dimensions of Nul(A) and (0) (3). How do the dimensions of Nul(A) and Call relate to the mber of columns of A?
2 3 -6 9 0 1 -2 0 3. Let A= 2 -4 7 2 The...
2 3 -6 9 0 1 -2 0 3. Let A= 2 -4 7 2 The RREF of A iso 0 1 3 -6 6 -6 0 0 0 (a) (6 points) Find a basis for Col A, the column space of A. 0 (b) (2 points) What is rank A? (c) (6 points) Find a basis for Null A, the null space of A. (d) (2 points) What is the dimension of the null space of A?
4 1 1. The matrix A and it reduced echelon form B are given below. 1-2...
4 1 1. The matrix A and it reduced echelon form B are given below. 1-2 95 4 10 3 0 0 1 -1 6 5 3 0 1 -3 0 -7 -2 0 -6 1 -2 0 0 0 1 -2 9 1-9 0 0 0 0 0 (a) Find p, q, r s t Nul A, Col A, Row A is a subspace of RP, R9, R', respectively Answer. p = 9= (b) Find a basis for Nul...
1. The matrix A and it reduced echelon form B are given below. 1-2 95 4...
1. The matrix A and it reduced echelon form B are given below. 1-2 95 4 [1 0 3 0 0 1 -1 6 5 -3 A= 0 1 -3 0 -7 -B= -2 0 -6 1 -2 0 0 0 1 -2 4 9 -9 0 0 0 0 0 (a) Find p, q, rs. Nul A, Col A, Row A is a subspace of R”, R9, R", respectively Answer.p = 9. r = (b) Find a basis for...
Please answer from part a through u The Fundamental Matrix Spaces: Consider the augmented matrix: 2...
Please answer from part a through u
The Fundamental Matrix Spaces: Consider the augmented matrix: 2 -3 -4 -9 -4 -5 6 7 6 -8 4 1 3 -2 -2 9 -5 -11 -17 -16 3 -2 -2 7 14 -7 2 7 8 12 [A[/] = 2 6 | -2 -4 -9 | -3 -3 -1 | -10 8 11 | 11 1 8 / 7 -10 31 -17 with rref R= [100 5 6 0 3 | 4...
4 1 1. The matrix A and it reduced echelon form B are given below. 1-2...
4 1 1. The matrix A and it reduced echelon form B are given below. 1-2 95 4 10 3 0 0 1 -1 6 5 3 0 1 -3 0 -7 -2 0 -6 1 -2 0 0 0 1 -2 91-9 0 0 0 0 0 (a) Find p, q, rs. Nul A, Col A, Row A is a subspace of R", R9, R', respectively Answer. p = 9=- (b) Find a basis for Nul A (c) Find...
Question 3. (20 pts) Let A= -3 9-27 2 -6 4 8 3 -9 -2 2 Find a basis for Col(A) and a basis for Nul(A). Question 4. (15 pts) Let the matrix A be the same as in Question 3. (1). Find the rank of A. (2). Find the dimensions of Nul(A) and Col(A). (3). How do the dimensions of Nul(A) and Col(A) relate to the number of columns of A?
A= 9 2 3 -9 -2 Question 4. (15 pts) Let the matrix A be the same as in Question 3 (1). Find the rank of A. (2). Find the dimensions of Nul(A) and Col(A). (3). How do the dimensions of Nul(A) and Col(A) relate to the number of columns of A?
6. (15 pts) For the linear system 3x + 2y + 10x = -6 3 + 2z = y+2z = 3 3+ 4y + 10% = 8 a) Use your calculator to place the augmented matrix in RREF and write it here. 3 2 10 -6 i 470 - 4 3 8 b) Find the general solution to the linear system, written as either the vector equation of a line or the vector equation of a plane.
Problem 1 Let A= 3 2 13 1 5 7 11 8 -3 9 10 -6 -4 12 8 a) [4 pts) Find a basis for N(A) in rational format. b) (3 pts) Find a particular solution to the matrix equation A*x= 5 -2 14 c) [3 pts] Use your answers in a), b) and the Superposition Principle to express the general solution in vector form to the matrix equation in b).
Question 3. (20 pts) Let A= -3 9-27 2 -6 48 3 -9 -2 2 Question 4. (15 pts) Let the matrix A be the same as in Question 3 (1). Find the rank of A (2). Find the dimensions of Nul(A) and (0) (3). How do the dimensions of Nul(A) and Call relate to the mber of columns of A?
2 3 -6 9 0 1 -2 0 3. Let A= 2 -4 7 2 The RREF of A iso 0 1 3 -6 6 -6 0 0 0 (a) (6 points) Find a basis for Col A, the column space of A. 0 (b) (2 points) What is rank A? (c) (6 points) Find a basis for Null A, the null space of A. (d) (2 points) What is the dimension of the null space of A?
4 1 1. The matrix A and it reduced echelon form B are given below. 1-2 95 4 10 3 0 0 1 -1 6 5 3 0 1 -3 0 -7 -2 0 -6 1 -2 0 0 0 1 -2 9 1-9 0 0 0 0 0 (a) Find p, q, r s t Nul A, Col A, Row A is a subspace of RP, R9, R', respectively Answer. p = 9= (b) Find a basis for Nul...
1. The matrix A and it reduced echelon form B are given below. 1-2 95 4 [1 0 3 0 0 1 -1 6 5 -3 A= 0 1 -3 0 -7 -B= -2 0 -6 1 -2 0 0 0 1 -2 4 9 -9 0 0 0 0 0 (a) Find p, q, rs. Nul A, Col A, Row A is a subspace of R”, R9, R", respectively Answer.p = 9. r = (b) Find a basis for...
Please answer from part a through u
The Fundamental Matrix Spaces: Consider the augmented matrix: 2 -3 -4 -9 -4 -5 6 7 6 -8 4 1 3 -2 -2 9 -5 -11 -17 -16 3 -2 -2 7 14 -7 2 7 8 12 [A[/] = 2 6 | -2 -4 -9 | -3 -3 -1 | -10 8 11 | 11 1 8 / 7 -10 31 -17 with rref R= [100 5 6 0 3 | 4...
4 1 1. The matrix A and it reduced echelon form B are given below. 1-2 95 4 10 3 0 0 1 -1 6 5 3 0 1 -3 0 -7 -2 0 -6 1 -2 0 0 0 1 -2 91-9 0 0 0 0 0 (a) Find p, q, rs. Nul A, Col A, Row A is a subspace of R", R9, R', respectively Answer. p = 9=- (b) Find a basis for Nul A (c) Find...
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