Find unknown element in a matrix

In summary, the purpose of finding an unknown element in a matrix is to determine its value for various mathematical and scientific calculations. This can be done using methods such as substitution, elimination, or matrix operations. Common techniques for finding unknown elements include Gaussian elimination, Cramer's rule, and matrix inversion, and key factors to consider include the given information, matrix size, and available operations. Software and programming languages such as MATLAB, Python, and R can also be used for this purpose.
  • #1
RedXIII
3
0

Homework Statement


Find all values of a for which the columns of the matrix are linearly dependent.

[tex]
\left( {\begin{array}{*{20}c}
2 & 0 & 8 \\
{ - 4} & 7 & a \\
1 & { - 3} & 4 \\
\end{array}} \right)
[/tex]


Homework Equations





The Attempt at a Solution


So I took of rref of the matrix and found

[tex]
\left( {\begin{array}{*{20}c}
1 & 0 & 4 \\
{ - 0} & 1 & 0 \\
0 & { 0} & a+16 \\
\end{array}} \right)
[/tex]

So then I have
a+16=0
a = -16


So that gives me 1 value which makes the columns of the matrix linearly dependent, but how do I find the other ones, or even know if more exist?

Thanks
 
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  • #2
RedXIII said:

Homework Statement


Find all values of a for which the columns of the matrix are linearly dependent.

[tex]
\left( {\begin{array}{*{20}c}
2 & 0 & 8 \\
{ - 4} & 7 & a \\
1 & { - 3} & 4 \\
\end{array}} \right)
[/tex]


Homework Equations





The Attempt at a Solution


So I took of rref of the matrix and found

[tex]
\left( {\begin{array}{*{20}c}
1 & 0 & 4 \\
{ - 0} & 1 & 0 \\
0 & { 0} & a+16 \\
\end{array}} \right)
[/tex]

So then I have
a+16=0
a = -16


So that gives me 1 value which makes the columns of the matrix linearly dependent, but how do I find the other ones, or even know if more exist?

Thanks

You've got it. There is just the one value, a=(-16). Otherwise the columns of the reduced matrix are linearly independent.
 

What is the purpose of finding an unknown element in a matrix?

The purpose of finding an unknown element in a matrix is to determine the value of a specific element that is missing or not given in a given matrix. This can be useful in various mathematical and scientific calculations or in solving problems related to data analysis and manipulation.

How do I find the unknown element in a matrix?

To find an unknown element in a matrix, you can use various methods such as substitution, elimination, or matrix operations. These methods involve using the given information in the matrix and performing mathematical operations to determine the value of the unknown element.

What are the common techniques used for finding unknown elements in a matrix?

The common techniques used for finding unknown elements in a matrix include Gaussian elimination, Cramer's rule, and matrix inversion. These techniques use different mathematical operations and algorithms to determine the value of the unknown element.

What are the key factors to consider when finding an unknown element in a matrix?

When finding an unknown element in a matrix, it is important to consider the given information in the matrix, the size of the matrix, and the available mathematical operations. It is also important to check for any potential errors or mistakes in the given information before starting the calculation process.

Can I use software or programming to find unknown elements in a matrix?

Yes, you can use various software programs or programming languages such as MATLAB, Python, or R to find unknown elements in a matrix. These programs have built-in functions and algorithms that can efficiently perform the necessary calculations and provide the value of the unknown element.

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