Matrices trouble, finding k so matrix is rank 2

In summary, a matrix is a rectangular array used to represent data and perform calculations. A matrix has rank 2 when it contains exactly 2 linearly independent rows or columns. It is important to find k for a matrix to have rank 2 as it helps understand the structure and properties of the matrix and can be used to solve problems and make predictions. The process for finding k involves manipulating the matrix using row operations. There are many real-world applications of finding k for a matrix to have rank 2, such as in data analysis, image processing, and signal processing.
  • #1
mr_coffee
1,629
1
Hello everyone, I have a problem...
I am suppose to Find the value of k for which the matrix:

A =
-4 9 14
2 7 16
-7 -2 k

has rank 2.
k = ?

I row reduced until i couldn't do it anymore and i got the following:
-4 9 14
0 23 46
0 0 92k + 2116

now I'm lost on how I'm suppose to find a value for k that will make this mantrix rank 2. ANy help would be great
 
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  • #2
Just put 92k + 2116 = 0 since the rank of the matrix is determined by the number of non-zero rows when in row echelon form.
 

FAQ: Matrices trouble, finding k so matrix is rank 2

What is a matrix?

A matrix is a rectangular array of numbers or symbols that are arranged in rows and columns. It is commonly used in mathematics, statistics, engineering, and other fields to represent data and perform calculations.

What does it mean for a matrix to have rank 2?

The rank of a matrix is the maximum number of linearly independent rows or columns it contains. If a matrix has rank 2, it means that there are exactly 2 linearly independent rows or columns in the matrix.

Why is it important to find k for a matrix to have rank 2?

Finding k for a matrix to have rank 2 is important because it helps us understand the structure and properties of the matrix. It can also be used to solve various problems and make predictions based on the data represented by the matrix.

What is the process for finding k to achieve rank 2 in a matrix?

The process for finding k to achieve rank 2 in a matrix involves manipulating the elements of the matrix using row operations (such as swapping rows, multiplying a row by a constant, or adding a multiple of one row to another) until the matrix has only 2 linearly independent rows or columns remaining.

Are there any real-world applications of finding k for a matrix to have rank 2?

Yes, there are many real-world applications of finding k for a matrix to have rank 2. For example, in data analysis and machine learning, finding the rank of a matrix can help determine the most important features or variables in a dataset. It can also be used in image processing, signal processing, and many other fields to extract relevant information and make predictions.

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