2. MATRIX:MATRIX: A rectangularA rectangular
arrangement ofarrangement of
numbers in rows andnumbers in rows and
columns.columns.
TheThe ORDERORDER of a matrixof a matrix
is the number of theis the number of the
rows and columns.rows and columns.
TheThe ENTRIESENTRIES are theare the
numbers in the matrix.numbers in the matrix. 





−
−
502
126
rows
columns
This order of this matrixThis order of this matrix
is a 2 x 3.is a 2 x 3.

3. 









−−
−
67237
89511
36402










−
−
3410
200
318 [ ]0759 −





 −
20
11











−
6
0
7
9
3 x 3
3 x 5
2 x 2 4 x 1
1 x 4
(or square
matrix)
(Also called a
row matrix)
(or square
matrix)
(Also called a
column matrix)

4. To add two matrices, they must have the sameTo add two matrices, they must have the same
order. To add, you simply add correspondingorder. To add, you simply add corresponding
entries.entries.










−
−
+










−
−
34
03
12
70
43
35










−++
++−
+−−+
=
)3(740
0433
13)2(5









 −
=
44
40
23

5. +





−
−
9245
3108






−
−
2335
2571
[ ])1(8 −+ 70 + 51+− 23+
55+− 34+ 32+ )2(9 −+
=
=
[ 7 7 4 5
0 7 5 7
]

6. To subtract two matrices, they must have the sameTo subtract two matrices, they must have the same
order. You simply subtract corresponding entries.order. You simply subtract corresponding entries.










−
−−









 −
232
451
704
831
605
429










−−−−
−−−−
−−−−
=
2833)2(1
)4(65015
740249










−
−−
=
603
1054
325

7. 









−
−−










−
−
724
113
810
051
708
342
[ []=
5-2
-4-1 3-8
8-3 0-(-1) -7-1
1-(-4)
2-0
0-7
=
2 -5 -5
5 1 -8
5 3 -7
]

8. In matrix algebra, a real number is often called aIn matrix algebra, a real number is often called a SCALARSCALAR..
To multiply a matrix by a scalar, you multiply each entry inTo multiply a matrix by a scalar, you multiply each entry in
the matrix by that scalar.the matrix by that scalar.






−
−
14
02
4






−
−
=
416
08






−
−
=
)1(4)4(4
)0(4)2(4

9. 













−
−
+




 −
−
86
54
30
21
2














−++
+−−
−=
)8(360
5241
2
=
[ [
[ ]
]]
-2
6
-3 3
-2(-3)
-5
==
-2(6) -2(-5)
-2(3) 6 -6
-12 10

10. 













−
−
+




 −
−
86
54
30
21
2














−++
+−−
−=
)8(360
5241
2
=
[ [
[ ]
]]
-2
6
-3 3
-2(-3)
-5
==
-2(6) -2(-5)
-2(3) 6 -6
-12 10