Matrix Variables: Solving Mx = b with 2-D Vectors

Thread starter EvLer
Start date Jan 29, 2007
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Matrix Variables

In summary, a variable in a matrix is a symbol or letter that represents an unknown quantity and is used in mathematical equations to solve for unknown elements. Variables can be used to express relationships, define systems of equations, and solve for multiple unknowns. Matrices can have more than one variable and variables can affect matrix operations by introducing unknown quantities and impacting the resulting matrix's size and structure. Variables in a matrix can be represented by any symbol or letter, including numbers and special characters.

Jan 29, 2007

EvLer

if I am given this to solve:
Mx = b
where M
[0 0]
[1 2]
[0 0]
[3 6]

and b = [b1, b2, b3, b4]^t

does that mean I have vector x as 4 elements, i.e. x1-x4 or just x1 and x2?

thanks

edit: oh, wait... rank is 2, so its only x1 and x2, right?

Last edited: Jan 29, 2007

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Jan 29, 2007

cristo

Staff Emeritus

Science Advisor

Your vector will be x=[x₁ x₂]^T

Jan 29, 2007

EvLer

oh, didn't refresh in time... thanks :)

1. What is a variable in a matrix?

A variable in a matrix refers to a symbol or letter that represents an unknown quantity within a matrix. It can take on different values and is often used in mathematical equations to solve for the unknown elements in a matrix.

2. How are variables used in matrices?

Variables are used in matrices to represent unknown quantities or to express relationships between different elements in a matrix. They can also be used to define systems of linear equations and solve for multiple unknowns simultaneously.

3. Can a matrix have more than one variable?

Yes, a matrix can have more than one variable. In fact, matrices with multiple variables are often used in advanced mathematical concepts such as linear algebra and optimization problems.

4. How do variables affect matrix operations?

Variables can affect matrix operations by introducing unknown quantities that need to be solved for. They can also impact the size and structure of the resulting matrix, especially when performing operations such as matrix multiplication or inversion.

5. Are variables in a matrix always represented by letters?

No, variables in a matrix can be represented by any symbol or letter. In some cases, numbers or special characters may also be used as variables to represent specific quantities or conditions within a matrix.