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?
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?
Question 3. (20 pts) Let A 3 2 3 9 -2 -6 4 8 -9 2 2 Find a basis for Col(A) and a basis for Nul(A).
+ Question Details 2 1 , and A = | V1 V2 V3 | . Is p in Nul A? Let v,-| 0 2 Yes, p is in Nul A No, p is not in Nul A 5.+ Question Details 2 2 10 2 1 0 30 0 2 41 4 2 16 3 Let A so that an echelon form of A is given by . Find a basis for Col A 1 0 3 1 0 0 0...
5 1 -2 0-4 Let A=0 0 0 0 13 1 -2 0 -3 5 a. Find a basis for Col A and find Rank A. b. Find a basis for Nul A.
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 2 0 1 10. Let A = 2 3 1 1 3 5 1 2 (a). Find the reduced row echelon form of A. (b). Using the answer for (a), find rank(A), and find a basis for Col(A). (c). Using the answer for (a), find a basis for Nul(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).
1-3 42 5 4 2 -6 9 8 . find bases 2 6 9-1 9 7 *6. Given A- find bases for nul A and col A -1 3 -4 25 -4 Express your answers in parametric vector form. 16 points
SOLVE A, B AND C!!
[1 2 0 1] 10. Let A = 2 3 1 1 |3.5 1 2 (a). Find the reduced row echelon form of A. (b). Using the answer for (a), find rank(A), and find a basis for Col(A). (c). Using the answer for (a), find a basis for Nul(A).