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Question 3 (2 points) Let A be the matrix defined below. 8 8 -8 1 -9...
Question 1 (1 point) Let A be the matrix defined below. -8 8 -8 1 -9...
Question 1 (1 point) Let A be the matrix defined below. -8 8 -8 1 -9 7 4 3 A= 7 6 -7 -9 4 9 5 5 -5 7 6 -7 -1 0 -7 -7 Suppose we know that ele 100 0 1 0 } RREFA= 10 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 Find a basis for the null space of A. O -87 6 5 O -9 9 -9 3...
Question 2 (1 point) The set B below is a basis for P2. Find the coordinate...
Question 2 (1 point) The set B below is a basis for P2. Find the coordinate vector of p(t) 3+t - 6t relative to B = {1-tt-t,2 – 2t+t} O 7 -3 o co 1 6 O 3 t 6t O 13 -10 Question 3 (2 points) Let A be the matrix defined below. -8 8 -8 1 -9 7 -7 7 4 3 A= 6 -9 4 9 -4 5 -5 5 6 -1 -7 -7 -7 0 Suppose...
Question 17 (2 points) Let A be a 3 x 4 matrix with a column space...
Question 17 (2 points) Let A be a 3 x 4 matrix with a column space of dimension 2. What is the dimension of the row space of A? Not enough information has been given. O 1/2 3 2. Question 16 (2 points) The rank of the matrix 1 2 - 1 2 4 2 1 2 3 is 02 O none of the given options Question 15 (2 points) Which of the following is not a vector space because...
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?
2. Let [8 Marks] 1 2 -1 1 3 -2 a) Find the null space of the matrix A and determine its dimension b) Find the range of...
2. Let [8 Marks] 1 2 -1 1 3 -2 a) Find the null space of the matrix A and determine its dimension b) Find the range of the matrix A and determine rank(A) c) State the rank-nullity theorem and verify that it is valid for the matrix A.
2. Let [8 Marks] 1 2 -1 1 3 -2 a) Find the null space of the matrix A and determine its dimension b) Find the range of the matrix A...
Question 3 [10 points] Consider the following matrix A and its reduced row-echelon form: A =...
Question 3 [10 points] Consider the following matrix A and its reduced row-echelon form: A = [-3 3 6 12 0 151 | 1 -1 -2 -4 0 -5 -6 3 9 15 12 18 rret(A) |-1 -1 0 -2 8 -3 [1 0 -1 -1 -4 -1] 01 1 3 -4 4 0 0 0 0 0 0 0 0 0 0 0 0 Find the dimensions of row(A), null(A), and col(A), and give a basis for each of...
Matrix Methods/Linear Algebra: Please show all work and justify the answer! 3 -6 9 0 1...
Matrix Methods/Linear Algebra: Please show all work and justify
the answer!
3 -6 9 0 1 -2 0 -6 3. Let A= 2 -4 7 2 The RREF of Aiso 0 1 2 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.
Question 3) (8 points) Consider the following matrix: A= ſi 4 0 0 28 3 12...
Question 3) (8 points) Consider the following matrix: A= ſi 4 0 0 28 3 12 2 11 -5 5 6 0 8 1 (a) Find a basis for the Rowspace(A). Then state the dimension of the Rowspace(A). (b) Find a basis for the Colspace(A). Then state the dimension of the Colspace(A). (e) Find a basis for the Nullspace(A). Then state the dimension of the Nullspace(A). (d) State and confirm the Rank-Nullity Theorem for this matrix.
Matrix Methods/Linear Algebra: Please show all work and justify the answer! Just need Part C, the...
Matrix Methods/Linear Algebra: Please show all work and justify
the answer! Just need Part C, the null Space and Part D please.
3 -6 9 0 1 -2 0 -6 3. Let A= 2 -4 7 2 The RREF of Aiso 0 1 2 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...
Part 1: Calculate the dimension Given the following matrix: 1 1 A 4 3 -2 4...
Part 1: Calculate the dimension Given the following matrix: 1 1 A 4 3 -2 4 5 -2 16 9-9 -4 4 3 4 -1 Let S be the space spanned by A, that is S span(A) The dimension of Sis: dim S = 1 Part 2: Find a basis Enter a basis B of S below. 0 | -3 7 B=BA 0 0 -1 1 0 0 0 0
Question 1 (1 point) Let A be the matrix defined below. -8 8 -8 1 -9 7 4 3 A= 7 6 -7 -9 4 9 5 5 -5 7 6 -7 -1 0 -7 -7 Suppose we know that ele 100 0 1 0 } RREFA= 10 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 Find a basis for the null space of A. O -87 6 5 O -9 9 -9 3...
Question 2 (1 point) The set B below is a basis for P2. Find the coordinate vector of p(t) 3+t - 6t relative to B = {1-tt-t,2 – 2t+t} O 7 -3 o co 1 6 O 3 t 6t O 13 -10 Question 3 (2 points) Let A be the matrix defined below. -8 8 -8 1 -9 7 -7 7 4 3 A= 6 -9 4 9 -4 5 -5 5 6 -1 -7 -7 -7 0 Suppose...
Question 17 (2 points) Let A be a 3 x 4 matrix with a column space of dimension 2. What is the dimension of the row space of A? Not enough information has been given. O 1/2 3 2. Question 16 (2 points) The rank of the matrix 1 2 - 1 2 4 2 1 2 3 is 02 O none of the given options Question 15 (2 points) Which of the following is not a vector space because...
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?
2. Let [8 Marks] 1 2 -1 1 3 -2 a) Find the null space of the matrix A and determine its dimension b) Find the range of the matrix A and determine rank(A) c) State the rank-nullity theorem and verify that it is valid for the matrix A.
2. Let [8 Marks] 1 2 -1 1 3 -2 a) Find the null space of the matrix A and determine its dimension b) Find the range of the matrix A...
Question 3 [10 points] Consider the following matrix A and its reduced row-echelon form: A = [-3 3 6 12 0 151 | 1 -1 -2 -4 0 -5 -6 3 9 15 12 18 rret(A) |-1 -1 0 -2 8 -3 [1 0 -1 -1 -4 -1] 01 1 3 -4 4 0 0 0 0 0 0 0 0 0 0 0 0 Find the dimensions of row(A), null(A), and col(A), and give a basis for each of...
Matrix Methods/Linear Algebra: Please show all work and justify
the answer!
3 -6 9 0 1 -2 0 -6 3. Let A= 2 -4 7 2 The RREF of Aiso 0 1 2 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.
Question 3) (8 points) Consider the following matrix: A= ſi 4 0 0 28 3 12 2 11 -5 5 6 0 8 1 (a) Find a basis for the Rowspace(A). Then state the dimension of the Rowspace(A). (b) Find a basis for the Colspace(A). Then state the dimension of the Colspace(A). (e) Find a basis for the Nullspace(A). Then state the dimension of the Nullspace(A). (d) State and confirm the Rank-Nullity Theorem for this matrix.
Matrix Methods/Linear Algebra: Please show all work and justify
the answer! Just need Part C, the null Space and Part D please.
3 -6 9 0 1 -2 0 -6 3. Let A= 2 -4 7 2 The RREF of Aiso 0 1 2 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...
Part 1: Calculate the dimension Given the following matrix: 1 1 A 4 3 -2 4 5 -2 16 9-9 -4 4 3 4 -1 Let S be the space spanned by A, that is S span(A) The dimension of Sis: dim S = 1 Part 2: Find a basis Enter a basis B of S below. 0 | -3 7 B=BA 0 0 -1 1 0 0 0 0
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