Exploring Determinants: Solving for a, b, c, g, h, i - Tips Included

In summary, the conversation discusses a question about finding determinants in a matrix and includes a brief discussion about a possible mistake in the question. The final conclusion is that the replacement of a variable with a constant does not affect the computation of the determinants.
  • #1
sara_87
763
0
Everyone is going to start to hate me know because i keep asking so many questions, but really i do look around these boards to help someone, but the questions are to hard for me or someone answers before me! :redface:

anyway my question is:

If the determinant of

a b c
d e f
g h i

is 7

then find the following determinants:

a)

a+2d b+2e c+2f
d e f
g h i

b)

a b c
g h i
d e f

c)

a b c
d e f
5g 5h 5i

My Answer:

i don't even know where to start!

any tips?
 
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  • #2
Those matrices bear resemblance to the original, don't they? ...
 
  • #3
yeah...
i still don't know what to do...
 
  • #4
You have been taught rules about how determinants change under row operations. Use them.
 
  • #5
wait, i wrote the question wrong (as usual, matt grime) the question is:

a b c
d e f
g h 1

is equal to 7

the other parts are the same.

if the question was the same as i had previously written it would i get:
a) =7
b) = -7
c) =35
 
  • #6
Looks correct.
 
  • #7
unfortunatley i wrote the question worng, in the book they replaced the i with 1...do you think that is a mistake?
 
  • #8
sara_87 said:
unfortunatley i wrote the question worng, in the book they replaced the i with 1...do you think that is a mistake?

Either way, it doesn't matter, since we don't need to know the actual value of i in order to compute the three determinants.
 

What are the determinants in a system with variables a, b, c, g, h, and i?

The determinants in a system with variables a, b, c, g, h, and i are the values that determine the behavior and outcome of the system. They represent the coefficients and constants in a system of equations and play a crucial role in solving for the variables.

Why is it important to solve for the determinants in a system?

Solving for the determinants in a system allows us to understand the relationship between the variables and how they affect the overall outcome. It also helps us to find the unique solution to the system of equations.

What are some tips for solving for the determinants in a system?

1. Make sure all equations are in standard form.2. Use elimination or substitution to reduce the number of variables.3. Use inverse operations to isolate the variables.4. Check your solution by plugging it back into the original equations.5. Practice and review different types of systems to become more familiar with the process.

Can the determinants in a system have multiple solutions?

Yes, the determinants in a system can have multiple solutions. This occurs when the equations are dependent on each other, meaning they are essentially the same equation. In this case, there are infinitely many solutions that satisfy the system of equations.

How can understanding determinants be applied in real-life situations?

Understanding determinants can be applied in various fields such as engineering, physics, economics, and computer science. It can be used to model and solve real-life problems, such as predicting the growth of a population, optimizing production processes, and analyzing data sets.

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