Alg1131W12T1 - Matrix arithmetic
Sunday, 27 May 2018
10:05 PM
Created with Microsoft OneNote 2016.
![Let's get you doing some basic arithmetic with matrices Here are two quick rules to remember.
• Rule 1: Matrices M and N can only be added or subtracted if they have the same size, which means same number m of rows; and same number n of columns.
For example, the matrix
1
8
3
-1
1
o
3
1
2
2
4
6
IS a
O matrix, and so could be added to or subtracted from any other
3X4
O matrix.
• Rule 2: Two matrices M and N can be multiplied in the order MI'V precisely when the number of columns of M equals the number of rows of N.
Thus if M is a 3 x 4 matrix, then it could be multiplied by N to get MINT provided that N was a matrix of size [select all that apply]
If an m x n matrix M is multiplied by an n x p matrix N v then the product MN is a mxp
Fill in the missing entries below to check that you understand how to do basic matrix arithmetic:
O
matrix.
1
i) If
2
1
5
O
—4
5
4
13
1
-2
8
4
—5
then a
_5
O and b
-2
1
7
c
13b
then c
2
14](Alg1131W12T1%20-%20Matrix%20arithmetic_files/image001.png)
![1
o
Consider the matrices A
1
apply]
1
1
-3
B
2
2
—3
4
1
—12
3
2
and D
6
—1
2
4
-1
o
2
O
4
Then which of the follow matrices is well-defined? [select all that
8
o
And which of these matrix products is well defined? [select all that apply]
DD-B
DB
DC-B
D D+2B.
CD
DC
DOB)
CA.
In the previous collection of product matrices; exactly one product is a 2 x 2 matrix. That product is explicitly the matrix
1
2
Note: the Maple notation for the matrix
3
4](Alg1131W12T1%20-%20Matrix%20arithmetic_files/image003.png)
