Elementary Linear Algebra (matrix)

In summary, the reduced row echelon form of the given matrix is |1 0| |0 1|, which can be obtained by using the given calculation rules and branching into three cases based on the values of sine and cosine of x.
  • #1
dazedoutpinoy
5
0

Homework Statement


Determine the reduced row echolon form of

| cos(x) sin(x) |
| -sin(x) cos(x) |

Homework Equations


you can interchange any two rows or columns, multiply a row or column by a nonzero number, add a multiple of one row or column to another


The Attempt at a Solution


|1 0|
|0 1|

is the solution but i couldn't figure out how to apply trig functions to equal 1 on the matrix
 
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  • #2
Ok, first off: I don't know what a "row echolon form" is. But using your calculation rules it is possible to obtain the identity.
What you first need to do (more specifically: What I had to do for my solution) is a case branching:

Case 1: sin(x) = 0:
Ok, I don't have to comment on this one, do I?

Case 2: cos(x) =0:
Your matrix is ((0,-1),(1,0)) (where I noted the two column-vectors in the inner parentheses). Using your modification rules you should easily get to the identity from there.

Case 3: Neither the sine nor the cosine term equal zero:
It's a few more steps but not too many. Two hints:
- cos(x) and sin(x) are non-zero numbers now, meaning you can (and actually must) multiply and divide by these terms.
- cos²(x) + sin²(x) = 1.
 
Last edited:

1. What is elementary linear algebra?

Elementary linear algebra is the study of linear equations and their solutions, using matrices and other algebraic techniques. It is a fundamental branch of mathematics that is used in various fields, such as engineering, physics, economics, and computer science.

2. What are matrices?

Matrices are rectangular arrays of numbers or symbols, arranged in rows and columns. They are used to represent systems of linear equations and perform operations such as addition, subtraction, and multiplication. Matrices are an essential tool in elementary linear algebra.

3. What is the difference between a row vector and a column vector?

A row vector is a matrix with only one row, while a column vector is a matrix with only one column. In other words, a row vector is a horizontal array of numbers, while a column vector is a vertical array of numbers. Both types of vectors are commonly used in linear algebra.

4. How is elementary linear algebra used in real life?

Elementary linear algebra has numerous applications in real life, such as in computer graphics, data analysis, and machine learning. It is also used in engineering to solve problems related to electrical circuits, mechanical systems, and structural analysis. Additionally, linear algebra is used in economics to model and analyze economic systems.

5. What are the basic operations in elementary linear algebra?

The basic operations in elementary linear algebra include addition, subtraction, multiplication, and division of matrices. Other important operations include finding the inverse of a matrix, calculating determinants, and solving systems of linear equations. These operations are used to manipulate and solve problems involving matrices and linear equations.

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