ADDITIONAL MATH-9
Determinants and Cramer’s Rule
I.
Find the determinant of the following matrix. Number 1 is done for you.
8 10
2 5
2. [
]
1. [
]
4 7
3 4
2 5
|
| = 2(4) – 5(3) = 8 − 15 = −7.
3 4
The determinant is -7.
3. [
3 −2
]
1 2
5. [
−9 8
]
−8 9
7. [
−2 2
]
3 −4
4. [
5 7
]
8 −9
6. [
2 3
]
−1 7
8. [
3 6
]
5 4
II.
Solve the following systems of equations. Identify if the system is consistent and
has one unique solution, the system is dependent and it has infinitely many
solutions or the system is inconsistent and has no solution.
Equation
1.
𝑥 + 3𝑦 = 7
−𝑥 + 3𝑦 = 7
2.
5 𝑥 + 3𝑦 = −9
2𝑥 − 5𝑦 = −16
3. 4𝑥 − 5𝑦 = 3
8𝑥 + 15𝑦 = −24
4.
𝑥+𝑦 =4
3𝑥 + 3𝑦 = 12
5.
5𝑥 + 2𝑦 = 7
10𝑥 + 4𝑦 = −3
System
(Consistent,
dependent
or
inconsistent)
Solution
Solve:
(One unique
solution,
infinitely
many
solution or no
solution)
Part III. Word Problem,
1. In a basket, there are 78 of mangoes and oranges in total. If the number of
mangoes is 24 less than the number of oranges, what is each number of
mangoes and oranges in the basket?