Algebra 2/Trig 4.1 Matrices
p. 216
Matrices – is a way to organize and list data using rows and columns.
A=
𝟒
𝟏
−𝟐
𝟎
𝟔
−𝟓
Dimensions are given by rows and columns.
Matrix A has 2 rows and 3 columns so it is a 2X3 Matrix
(4,1) (-2,0) (6,-5)
Each entry in the matrix is represented by a lower case letter (same
letter as the matrix) and the location
a13 – is an entry in the first row, and third column.
a13=6
1
Square Matrix
1 −5 7
A= 0 2 −3
6 −4 −2
3X3 Matrix
5 −2
B= 7 −5
0 2
3
1
−4
3X3 Matrix
Since the matrices have the same dimensions, we can perform
addition and subtraction.
A+B= we add corresponding entries
6 −7 10
A+B= 7 −3 −2
6 −2 −6
Is A+B=B+A
Yes, by the commutative Property
Subtraction
1 −5 7
A= 0 2 −3
6 −4 −2
5 −2
B= 7 −5
0 2
3
1
−4
2
−4 −3 4
A-B= −7 7 −4
6 −6 2
4
3 −4
B-A= 7 −7 4
−6 6 −2
A-B and B-A are additive inverses
Scalar Multiplication
2
1 −6
A= 5
4
0
−3 −2 3
Find 5A:
2
5 5
−3
1 −6
4
0
−2 3
=
10
5
−30
25
20
0
−15 −10 15
Examples
2
1 −6
A= 5
4
0
−3 −2 3
1
5
B= 3
0
−2 −1
2
−4
6
3
Find:
1.) A+B
2.) 2A-3B
3
5
𝐴 + 8 𝐵 (exact solutions)
4
3.)
Solve for x and y:
18
−2
9
𝑦
1
𝑥
24
15
=
2𝑥 + 6
2
3
1
4
−5𝑦
H.W. p. 221 – 223. Problems: 12 – 44 EVENS
50-54
59-62
4