Given that the matrix A has the reduced row echelon form U: 1 0 3 0 -2 1 0 0 0 0 1 0 0 0 0 2 1 7 2 -2 3 0 3 -9 0 1 4 A = U = –1 1 -2 -1 7 -1 - 2 3 9 4 4 note: you do not need to do any row operations, they are done already!] (a) What is the rank of A? (b) What is the nullity of A? (c) Find a basis for the row space of A. (d) Find a basis for the column space of A. (e) Find a basis for the null space of A. (f) What is the nullity of A"? [Hint: no row ops required]
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
please solve for parts D, E, and F.
![1. Given that the matrix A has the reduced row echelon form U:
1 030 -2
1 0
0 0 0
0 0 0 0
2
1
7
2 -2
3 0
9.
3 -9
1
4
A =
U :
-1
1
-2
-1
7
1
-1
2 3
4
4
[note: you do not need to do any row operations, they are done already!]
(a) What is the rank of A?
(b) What is the nullity of A?
(c) Find a basis for the row space of A.
(d)
Find a basis for the column space of A.
(e) Find a basis for the null space of A.
(f) What is the nullity of AT? [Hint: no row ops required]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8d14a18-18b6-4b9f-91b0-8c8acc9b34e2%2Fd6431e6e-7588-4eb1-87c3-dadcfb230cd4%2Fvlx55w8_processed.png&w=3840&q=75)
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