2. Unit Learning Outcome 3
Perform Operation on matrices.
Matrix
Inverse of Matrix
IBM111 - Inverse of Matrix
3. a.What is a matrix?
a. A matrix is a rectangular grid of numbers arranged
into rows and columns.
IBM111 - Inverse of Matrix
4. a. Inverse of a matrix?
What is an inverse matrix?
• The Inverse of a matrix is always a matrix.
• The inverse of the matrix follows the same order of its
original matrix.
• The invers of a matrix is always true for a square matrix
• The Inverse of a matrix exist if the determinant of
said matrix is not equal to zero
• The inverse of matrix is just the opposite of the
original matrix.
IBM111 - Inverse of Matrix
5. b. Graphical representation of application.
• Creating secret message using numbers with inverse
matrix. (encoding and decoding messages).
IBM111 - Inverse of Matrix
6. Why is it important?
RealWorld Application of the topic.
• Creating secret message using numbers with
inverse matrix. (encoding and decoding
messages).
• Computer graphics in the 3D space use
matrices to render what we see on the
screen.
IBM111 - Inverse of Matrix
7. Encoding and decoding message
a. For instance SELL NOW is the encoded
message.
• Numbers representing the encoded message
19, 5, 12, 12, 0, 14, 15, 23
• Above is less effective, lets twist to make it a bit
complicated
19 12 0 15
5 12 14 23
IBM111 - Inverse of Matrix
8. • Now we multiply the encoded matrix with the original matrix.
82 96 70 160
29 36 28 61
Original
• Multiply with a 2x2 matrices by picking random numbers.
Pick, 3, 1, 5 and 2, and they’re also known as the coding
matrix.
A B
3 5
1 2
x
19 12 0 15
5 12 14 23
2 −5
−1 3
82 96 70 160
29 36 28 61
• Multiply matrix C with matrix D to find the original
message matrix.
IBM111 - Inverse of Matrix
9. • Substitute the values with letters respectively
• SELL NOW is the encrypted message.
19 12 0 15
5 12 14 23
19 5 12 12 0 14 15 23
S E L L - N O W
IBM111 - Inverse of Matrix
10. An example of the type of work done in
theTopic?
a. Give a mathematical walk through of the
concepts learnt in thisTopic.
• Defining what inverse of matrix is.
• Why inverse matrix are important.
• Recap on operations used in matrix.
• Inverse of a matrix notation.
• Inverse of a 1x1, 2x2 and a 3x3 matrix.
IBM111 - Inverse of Matrix
11. New knowledge was gained
My experience learning theTopic and the
effect it will have on my studies here in
WPU :
• NewTopic to me.
• Benefit me not only in this institution but after here.
• For instance the idea of encoding and
decoding messages.
IBM111 - Inverse of Matrix
