Robbie W.
Discrete Math
03/07/03
Matrices Made Easy
Chapter 3
Section 1-3: Addition, Subtraction and Multiplication of Matrices
Matrix terminology:
Element: an individual entry, also called a component
Order: the dimension, ex: 3 by 2
Square matrix: the dimensions are the same, ex: 4 by 4
Column Matrix AKA Column Vector: the matrix is a column ex: 3 by 1
Row Matrix AKA Row Vector: the matrix is a row ex: 1 by 3
Problem # 1: Add these two matrices together
| 9 | 4 | 6 |
| 7 | 1 | 5 |
10 |
2 |
8 |
| 5 | 11 | 2 |
Explanation for Problem # 1:
First Step: Take 9 from the first matrix and add it to 10 from the second
matrix, 9 + 10 =19
Second Step: Take 4 from the first matrix and add it to 2 from the second
matrix, 4 + 2 =6
Repeat these steps for the rest of the elements
Answer:
| 19 | 6 | 14 |
| 12 | 12 | 7 |
Problem # 2: Take the two matrices from the first problem
and subtract them
Explanation for Problem # 2:
First Step: Take 9 from the first matrix and subtract it from the 10 in the
second matrix, 9 - 10 =-1
Second Step: Take the 4 from the first matrix and subtract it from the 2 in the
second matrix, 4 - 2 =2
Repeat these steps for the rest of the elements
Answer:
| -1 | 2 | -2 |
| 2 | -10 | 3 |
Problem # 3: Multiply these two matrices together
| 4 | 7 |
| 1 | 0 |
0 |
-3 |
| 2 | -1 |
Explanation for Problem # 3:
First Step: Take the 4 in the first matrix and multiply it by the 0 in the
second matrix, 4 x 0 =0, then take the 7 from the first matrix and multiply it
by the 2 in the second matrix, 7 x 2 =14, finally take the 0 and 14 and add
those together to get the first number, 0 + 14 =14
Second Step: Take the 4 in the first matrix and multiply it by -3 from the
second matrix, 4 x -3 =-12, then take the 7 from the first matrix and multiply
it by the -1 from the second matrix, 7 x -1 =-7, then add the -12 and the -7,
-12 +-7 =-19
Third Step: Take the 1 from the first matrix and multiply it by the 0 in the
second matrix, 1 x 0 =0, then take the 0 from the first matrix and multiply it
by the 2 in the second matrix, 0 x 2 =0, add these two numbers together, 0 + 0
=0
Fourth Step: Take the 1 from the first matrix and multiply it by the -3 in the
second matrix, 1 x-3=-3, then tae the 0 from the second matrix and multiply it
by -1, 0 x -1 =0, add these two numbers together, -3 + 0 = -3
Answer:
| 14 | -19 |
| 0 | -3 |
Quote of the Day
A mathematician of the first rank, Laplace quickly revealed himself as only a
mediocre administrator; from his first work we saw that we had been deceived.
Laplace saw no question from its true point of view; he sought subtleties
everywhere; had only doubtful ideas, and finally carried the spirit of the
infinitely small into administration.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc.,
1988.
This quote was found at http://math.furman.edu/~mwoodard/ascquotn.html