Augmented Matrix: Understanding Notation and Examples

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In summary, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is commonly used in mathematics, physics, and computer science to represent and manipulate data or equations. Matrices are used to perform operations such as addition, subtraction, multiplication, and inversion, which are important in solving linear equations and representing transformations in geometry. They are typically represented by enclosing their elements in square brackets and separating them by commas. In computer graphics, matrices are used to represent and manipulate 2D and 3D objects, such as rotating, scaling, and translating objects, as well as performing lighting and shading calculations. There is a difference between a row matrix and a column matrix, with a row matrix having only one
  • #1
KataKoniK
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They do not seem to mention this case in the book, but if they say A is an augmented 3x5 matrix, then does it look like the following?

1 0 0 0 0 | 0
0 1 0 0 0 | 0
0 0 1 0 0 | 0

or

1 0 0 0 | 0
0 1 0 0 | 0
0 0 1 0 | 0

I'm a bit confused. If they say 6 columns that includes the constants columns as well?

So another example, this matrix is 2x3?

1 0 | 0
0 1 | 0
 
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  • #2
Yes- when referring to an "augmented matrix", the "count" of columns includes the "augmented" column. That is:
1 0 0 0 | 0
0 1 0 0 | 0
0 0 1 0 | 0
is "3 x5"- 3 rows, 5 columns.
and
1 0 | 0
0 1 | 0
is "2 x3".

1 0 0 0 0 | 0
0 1 0 0 0 | 0
0 0 1 0 0 | 0
would be "3x 6", not "3x 5".
 
  • #3
Thanks for the clarification :)
 

1. What is a matrix?

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is commonly used in mathematics, physics, and computer science to represent and manipulate data or equations.

2. What is the purpose of a matrix?

Matrices are used to perform operations such as addition, subtraction, multiplication, and inversion, which are important in solving linear equations and representing transformations in geometry.

3. How is a matrix represented?

A matrix is typically represented by enclosing its elements in square brackets and separating them by commas. For example, [1 2 3; 4 5 6; 7 8 9] is a 3x3 matrix with elements 1, 2, 3 in the first row, 4, 5, 6 in the second row, and 7, 8, 9 in the third row.

4. What is the difference between a row matrix and a column matrix?

A row matrix has only one row and multiple columns, while a column matrix has only one column and multiple rows. Row matrices are used for representing vectors, while column matrices are used for representing transformations.

5. How are matrices used in computer graphics?

Matrices are used in computer graphics to represent and manipulate 2D and 3D objects. They can be used to rotate, scale, and translate objects, as well as perform lighting and shading calculations.

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