What Values of k Affect the Solutions of This Matrix System?

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In summary, a matrix is a rectangular array used to organize and manipulate data in mathematical and scientific applications. It is important in science as it allows for efficient representation and operations on data. In a matrix, "K" is typically used as a constant or variable and can be found by solving equations involving it. Real-world applications of matrices include population growth models, quantum mechanics, image processing, and financial analysis in various fields of science.
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RajdeepSingh7
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Question :
Consider the following augmented matrix for a system of linear equations.
1 2 3 | 4 
0 1 2  3 |
| 0 0 k − 1  0 |
0 0 0 | k^2−1 

where k is some real number. For which values of k does the system have
(a) no solutions?
(b) infinitely many solutions?
(c) a unique solution?
[ Better version available here ---> http://imageshack.us/photo/my-images/839/screenshot20120416at636.png/ ]


Answer:

a) k is not equal to 1 or -1
b) k = 1
c) k =-1


Just wanted to see if I had it right, and had missed anything, as I had a bit of deliberation for the answers :)
 
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  • #2
Yes, that is correct.
 

FAQ: What Values of k Affect the Solutions of This Matrix System?

What is a matrix?

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is used to organize and manipulate data in various mathematical and scientific applications.

What is the importance of matrix in science?

Matrices are important in science because they can represent data in a more organized and efficient way. They are also used in various mathematical operations, such as solving systems of equations, calculating transformations, and analyzing data in statistics.

What is the role of "K" in a matrix?

In a matrix, "K" usually represents a constant or variable that is used in mathematical operations. It can also be used to represent a specific value or parameter in a given situation or problem.

How do you find the values of "K" in a matrix?

The values of "K" in a matrix can be found by solving the equations or systems of equations that involve "K". This can be done by using various mathematical techniques, such as substitution, elimination, or matrix operations.

What are some real-world applications of matrices?

Matrices have a wide range of applications in various fields of science, such as physics, chemistry, biology, engineering, and economics. Some specific examples include population growth models, quantum mechanics, image processing, and financial analysis.

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