Homework Answers
first we find row reduced
echelon form of A.then the pivot coloumns are 1,2 so the coloumns
of A corresponds to pivot coloumns will span coloumnspace of A.
ii) we write b as a linear combination of vectors in the basis of Coloumnspacw of A,such a,b exist so b is in col A.
۷/د 3 ماده 2 م م م 4 : له ي : و ویک/ A۸۵ Crew)...
۷/د 3 ماده 2 م م م 4 : له ي : و ویک/ A۸۵ Crew) The crank DE of the four-bar linkage shown in Fig. 2-6 has a constant angular velocity of 4 rad/s CCW. At the Inseanc shown, determine (a) the angular velocity Link BD and (b) angular velocity of link AB. FIND : CALL Ilci's) B R3 = 5 ft 3 D CALCULATE 24 = 4 rad/s Waolo VBA Fig. 2-6 Kinematic schematic representation of a four-bar...
2 -2 2 2 2) A2 3 1 1 6 -6 7 7 2) 1 1-11...
2 -2 2 2 2) A2 3 1 1 6 -6 7 7 2) 1 1-11 1. What is the deteminant of A? 3. Find a basis for Col A? 4. Find a basis of NULA 6 List 6 vectors in Col A. How many vectors belonging to Nul A that you can list? Why?
1. Consider the following Linear transformation L : R5 + R5 represented in the standard basis...
1. Consider the following Linear transformation L : R5 + R5 represented in the standard basis via the following matrix: 1 7 4 1 A= 2 4 6 9 -4 0 3 4 3 3 6 12 0 1 9 8 7 9 -2 0 2 (a) Find a basis for Null(A), Col(A), and Row(A). (b) For each v in your basis for Col(A) find a vector u ER5 do that Au = v. (c) Show that the vectors you...
1. Consider the matrix 12 3 4 A 2 3 4 5 3 4 5 6...
1. Consider the matrix 12 3 4 A 2 3 4 5 3 4 5 6 As a linear transformation, A maps R' to R3. Find a basis for Null(A), the null space of A, and find a basis for Col(A), the column space of A. Describe these spaces geometrically. 2. For A in problem 1, what is Rank(A)?
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?
Find a basis for the column space of the matrix [-1 3 7 2 0 |1-3...
Find a basis for the column space of the matrix [-1 3 7 2 0 |1-3 -7 -2 -2 1 Let A = 2 -7 -1 1 1 3 and B 1 -4 -9 -5 -3 -5 5 -6 -11 -9 -1 0 0 0 0 It can be shown that matrix A is row equivalent to matrix B. Find a basis for Col A. 3 7 -2 -7 -4 -11 2 -9 -6 -7 -3 0 1 0 0...
Problem 2 [2 4 6 81 Let A 1 3 0 5; L1 1 6 3 a) Find a basis for the nullspace of A b) Find the basis for the rowspace of A c) Find the basis for the range of A that consists of column vectors of...
Problem 2 [2 4 6 81 Let A 1 3 0 5; L1 1 6 3 a) Find a basis for the nullspace of A b) Find the basis for the rowspace of A c) Find the basis for the range of A that consists of column vectors of A d) For each column vector which is not a basis vector that you obtained in c), express it as a linear combination of the basis vectors for the range of...
1 2 -3 1 -6 -2 5 2. 4. (10 points) Let A = (a) (5...
1 2 -3 1 -6 -2 5 2. 4. (10 points) Let A = (a) (5 points) Find a basis for col(A) and calculate rank(A). (b) (5 points) Find a basis for null(A) and calculate nullity(A).
Find a basis for Col(A) and a basis for Nul(A) Question 3. (20 pts) Let A=...
Find a basis for Col(A) and a basis for Nul(A)
Question 3. (20 pts) Let A= 3 9-27 2-6 18 3 9 -2 2 Find a basis for Col(A) and a basis for Nul(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?
۷/د 3 ماده 2 م م م 4 : له ي : و ویک/ A۸۵ Crew) The crank DE of the four-bar linkage shown in Fig. 2-6 has a constant angular velocity of 4 rad/s CCW. At the Inseanc shown, determine (a) the angular velocity Link BD and (b) angular velocity of link AB. FIND : CALL Ilci's) B R3 = 5 ft 3 D CALCULATE 24 = 4 rad/s Waolo VBA Fig. 2-6 Kinematic schematic representation of a four-bar...
2 -2 2 2 2) A2 3 1 1 6 -6 7 7 2) 1 1-11 1. What is the deteminant of A? 3. Find a basis for Col A? 4. Find a basis of NULA 6 List 6 vectors in Col A. How many vectors belonging to Nul A that you can list? Why?
1. Consider the following Linear transformation L : R5 + R5 represented in the standard basis via the following matrix: 1 7 4 1 A= 2 4 6 9 -4 0 3 4 3 3 6 12 0 1 9 8 7 9 -2 0 2 (a) Find a basis for Null(A), Col(A), and Row(A). (b) For each v in your basis for Col(A) find a vector u ER5 do that Au = v. (c) Show that the vectors you...
1. Consider the matrix 12 3 4 A 2 3 4 5 3 4 5 6 As a linear transformation, A maps R' to R3. Find a basis for Null(A), the null space of A, and find a basis for Col(A), the column space of A. Describe these spaces geometrically. 2. For A in problem 1, what is Rank(A)?
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?
Find a basis for the column space of the matrix [-1 3 7 2 0 |1-3 -7 -2 -2 1 Let A = 2 -7 -1 1 1 3 and B 1 -4 -9 -5 -3 -5 5 -6 -11 -9 -1 0 0 0 0 It can be shown that matrix A is row equivalent to matrix B. Find a basis for Col A. 3 7 -2 -7 -4 -11 2 -9 -6 -7 -3 0 1 0 0...
Problem 2 [2 4 6 81 Let A 1 3 0 5; L1 1 6 3 a) Find a basis for the nullspace of A b) Find the basis for the rowspace of A c) Find the basis for the range of A that consists of column vectors of A d) For each column vector which is not a basis vector that you obtained in c), express it as a linear combination of the basis vectors for the range of...
1 2 -3 1 -6 -2 5 2. 4. (10 points) Let A = (a) (5 points) Find a basis for col(A) and calculate rank(A). (b) (5 points) Find a basis for null(A) and calculate nullity(A).
Find a basis for Col(A) and a basis for Nul(A)
Question 3. (20 pts) Let A= 3 9-27 2-6 18 3 9 -2 2 Find a basis for Col(A) and a basis for Nul(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?
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