Matrix Determinant and Equations

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Questions and Answers

What is the determinant of the matrix represented by the values:\n``` 1 2 3 3 1 5 -4 8 12

-18 (correct)
0
24
36

Using the demand function -15p + 250 = q, what is the value of q when the price p is $10?

100 (correct)
1000
250
400

What is the equilibrium price in the market when solving the equations -15p + 250 = q and 25p - 150 = q using determinants?

12
10
14
8 (correct)

After calculating the equilibrium quantity using matrices, what value is obtained when p is substituted into either the demand or supply function?

<p>80 (C)</p> Signup and view all the answers

Which property of determinants is used to simplify the calculation when finding the determinant of the matrix given?

<p>Adding a multiple of one row to another does not change the determinant. (A)</p> Signup and view all the answers

Flashcards

Determinant of a 3x3 Matrix

A scalar value calculated from the elements of a square matrix, used in various mathematical applications, including solving systems of linear equations and finding inverses of matrices.

Equilibrium Price

The price at which the quantity demanded equals the quantity supplied in a market, representing a stable market condition.

Equilibrium Quantity

The quantity of a good or service that is bought and sold at the equilibrium price.

Demand Function

An equation that expresses the relationship between the price of a good and the quantity demanded of that good at a certain time.

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Supply Function

An equation that describes the relationship between price and quantity supplied of a good, reflecting the producers' behavior.

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Matrix Solution for Equilibrium

Using matrix methods to find the equilibrium price and quantity in a market by representing the demand and supply functions as a system of linear equations, and solving.

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Determinant Solution for Equilibrium

Using determinants of matrices to find the equilibrium price and quantity by representing the demand and supply functions as a system of linear equations, and solving.

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Study Notes

Matrix Determinant

A matrix is given:

1  2  3
3  1  5
- 4 8 12

System of Equations

Two equations are given relating variables p and q:
- -15p + 250 = q
- 25p - 150 = q

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Description

Test your knowledge on calculating matrix determinants and solving systems of equations with the variables p and q. This quiz covers both matrix operations and linear algebra concepts. Challenge yourself to find the solutions!