2 1 [2 0 0 1 0 0 2 2 1 6 [i 1 -2 3] 0 1] 1' 1. If A = 3 and B = 1 then 1 -1 2 -2 -3 2 3 2] a) Find the sum of the cofactors of A23 and B4. b) Find IAl.
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.
![KFUPM – PREP MATH PROGRAM – MATH002 – TERM 203
11.4 Recitation Exercises
[2 0
0 1
6.
1]
2
1
2
3.
and B =
1
-1
, then
1
1. If A =
-1 2
[-3 2
1
-2
[1 1
-2
3]
3
2.
a) Find the sum of the cofactors of A23 and B44.
b) Find IAl.
2. Evaluate the following determinants
12
|3 0 0|
c)
2 1 1
|1 2 21
a)
b)
4
1
|7 3 -2l
14 0
5
2 0
li 0 2
1|
-13
-3|
4
c)
e)
|-2
1
4
-2
6.
21
31
3. Let A and B be 4 x 4 invertible matrices. Determine wither each of the following
statements is true or false:
a)
|A²| = |A|?
b) |2B| = 8|B|
c)
|A.B| = |A|. |B|
d) |A + B| = |A|+ |B|
e) IInl = 1
f) |A-| = |A|.
4. If det(M – xl) = 0, M = l and I =
then x =
A) 1
B) 2
C) 3
D) -1
E) -1/2.
5. If A and B are 3 x 3 matrices such that |A| = 5 and |B| = -2, then
|3(A B²)-'| =
27
15
-30
10
A)
В)
C)
D)
E) 540
20
10
27](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faee2279c-3ded-4856-af66-07025f1971fd%2Fcc6b1175-903b-45c9-ae67-80907598b0c1%2Fxp6cj2_processed.jpeg&w=3840&q=75)
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