matrix - a rectangular array of numbers or symbols which are generally arranged in rows and columns

Basic m x n Matrix Operations

Given 2 matrices |A| and |B|, this performs the following basic matrix operations

* Matrix Addition |A| + |B|

* Matrix Subtraction |A| - |B|

* Matrix Multiplication |A| x |B|

* Scalar multiplication rA where r is a constant.

* Matrix Addition |A| + |B|

* Matrix Subtraction |A| - |B|

* Matrix Multiplication |A| x |B|

* Scalar multiplication rA where r is a constant.

Digraph Items

Given a digraph, this determines the leader, and symmetric matrix.

Finance

1) [URL='http://www.mathcelebrity.com/npv.php?matrix1=0%2C-8000%0D%0A1%2C3500%0D%0A2%2C3500%0D%0A3%2C3500%0D%0A&irr=8&pl=NPV']Net present value[/URL] = $1,019.85
[URL='http://www.mathcelebrity.com/npv.php?matrix1=0%2C-8000%0D%0A1%2C3500%0D%0A2%2C3500%0D%0A3%2C3500&irr=8&pl=IRR']IRR[/URL] = 14%
I need a reinvestment rate from you for [URL='http://www.mathcelebrity.com/mirr.php']MIRR shown here[/URL]
Yes, we should pursue the project since NPV > 0
2) [URL='http://www.mathcelebrity.com/npv.php?matrix1=0%2C-8000%0D%0A1%2C5000%0D%0A2%2C5000&irr=8&pl=NPV']Net present value[/URL] = $916.32
Buy A as it has the higher net present value.

Find the elements on the principal diagonal of matrix B

Find the elements on the principal diagonal of matrix B
Matrix B:
|0 0 8|
|-1 3 0|
|2 -5 -7|
The main diagonal is any entry where row equals column
|[B]0[/B] 0 8|
|-1 [B]3 [/B] 0|
|2 -5 [B]-7[/B]|
In this case, it is [B]0, 3, -7[/B]

Markov Chain

Given a transition matrix and initial state vector, this runs a Markov Chain process.

Matrix Properties

Given a matrix |A|, this calculates the following items if they exist:

* Determinant = det(A)

* Inverse = A^{-1}

* Transpose = A^{T}

* Adjoint = adj(A)

* Eigen equation (characteristic polynomial) = det|λI - A|

* Trace = tr(A)

* Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form

* Dimensions of |A| m x n

* Order of a matrix

* Euclidean Norm ||A||

* Magic Sum if it exists

* Determines if |A| is an Exchange Matrix

* Determinant = det(A)

* Inverse = A

* Transpose = A

* Adjoint = adj(A)

* Eigen equation (characteristic polynomial) = det|λI - A|

* Trace = tr(A)

* Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form

* Dimensions of |A| m x n

* Order of a matrix

* Euclidean Norm ||A||

* Magic Sum if it exists

* Determines if |A| is an Exchange Matrix

Solving word problems with the matrix method?

Hello everyone.
I am stuck on a work question that we are required to solve using the matrix (or Gauss-Jordan) method.
[CENTER]"A car rental company wants to buy 100 new cars. Compact cars cost $12,000 each,
intermediate size cars cost $18,000 each, full size cars cost $24,000 each, and the company
has a budget of $1,500,000. If they purchase twice as many compact cars as intermediate
sized cars, determine the number of cars of each type that they buy, assuming they
spend the entire budget."
[/CENTER]
I am fairly certain that I could solve this easily, except I cannot figure out the proper three equations that correspond to this question. I someone could help me figure them out, it would be greatly appreciated!