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Algebra 2
Today:• Class Announcements• PLAN Practice• 4.1 Notes• Begin Homework• Show Chapter 3 Test Scores
Vocabulary:entry, scalar multiplications
4.1 – Matrix Operations
Objectives:• Identify the characteristics of a
matrix• Add and subtract matrices• Multiply scalars • Solve a matrix equation
Anatomy of a Matrix (Matrices)
Identifying the dimensions of a matrix: # of Rows x # of Columns
a b c d
e f g hRows
Columns
A is a 2x3 matrix
210
246A
Identify this matrix:
02
53BB is a 2x2 matrix
Anatomy of a Matrix (Matrices)
Identify this matrix:
119422
30411
11023
CC is a 3x5 matrix
A is a 2x3 matrix
210
246A
Anatomy of a Matrix (Matrices)
Identify this matrix:
210
412
312
132
DD is a 4x3 matrix
A is a 2x3 matrix
210
246A
Anatomy of a Matrix (Matrices)
Identify this matrix:
7
2
3
Ecolumn matrix
A is a 2x3 matrix
210
246A
Anatomy of a Matrix (Matrices)
Identify this matrix:
0232F row matrix
A is a 2x3 matrix
210
246A
Anatomy of a Matrix (Matrices)
Identify this matrix:
321
310
543
Gsquare matrix
A is a 2x3 matrix
210
246A
Anatomy of a Matrix (Matrices)
Identify this matrix:
00
00
00
Hzero matrix
A is a 2x3 matrix
210
246A
Anatomy of a Matrix (Matrices)
c1b
24aJ
210
246A
Matrices are equal if they are the same size and each entry is equal.
Anatomy of a Matrix (Matrices)
210
246A
c1b
24aJ
6 4 -2 a 4 -2=0 1 2 b 1 c
a = 6b = 0c = 2
Anatomy of a Matrix (Matrices)
Find a, b, and c if A = J.
3-y1x
242zK
210
246A
Matrices are equal if they are the same size and each entry is equal.
Anatomy of a Matrix (Matrices)
210
246A
3-y1x
242zK
2z 4 -26 4 -2=x 1 y-30 1 2
x = 0y = 5z = 3
Find x, y, and z if A = K.
Anatomy of a Matrix (Matrices)
Adding and Subtracting MatricesTo add or subtract matrices:
1. Matrices same size2. Add/subtract same entries
3-810
226-M
12
43N
51
00
23
P
10
52Q
523
024R
Find:L + M
6 4 -2L=0 1 2
0 6 -4
10 9 -1
Find:M + NNot possible; sizes not equal
To add or subtract matrices:1. Matrices same size2. Add/subtract same entries
3-810
226-M
12
43N
51
00
23
P
10
52Q
523
024R
Adding and Subtracting Matrices
6 4 -2L=0 1 2
Find:N + RNot possible; sizes not equal
To add or subtract matrices:1. Matrices same size2. Add/subtract same entries
3-810
226-M
12
43N
51
00
23
P
10
52Q
523
024R
Adding and Subtracting Matrices
6 4 -2L=0 1 2
Find:M – R
-2 0 -2
13 10 -8
To add or subtract matrices:1. Matrices same size2. Add/subtract same entries
3-810
226-M
12
43N
51
00
23
P
10
52Q
523
024R
Adding and Subtracting Matrices
6 4 -2L=0 1 2
Find:P – LNot possible; sizes not equal
Add and Subtracting MatricesTo add or subtract matrices:1. Matrices same size2. Add/subtract same entries
3-810
226-M
12
43N
51
00
23
P
10
52Q
523
024R
6 4 -2L=0 1 2
Find:Q – N
1 1
2 0
Add and Subtracting MatricesTo add or subtract matrices:1. Matrices same size2. Add/subtract same entries
3-810
226-M
12
43N
51
00
23
P
10
52Q
523
024R
6 4 -2L=0 1 2
Multiply ScalarsTo multiply a scalar:1. Multiply the scalar with every
entry
Perform the scalar multiplication:
210
2466
21
343-
36 24 -12
0 6 12
-12 -9
3 -6
Solving a Matrix EquationTo solve a matrix equation:1. Simplify both sides of the
equation.2. Set up equations and solve3. Present answers4. Check
Solve:
80
48-48
61
2x-4
2y1-
084
x = 6, y = -2
To solve a matrix equation:1. Simplify both sides of the
equation.2. Set up equations and solve3. Present answers4. Check
Solve:
2118
9-0
11-
5x
4y5
2103
x = 10, y = 2
Solving a Matrix Equation
Assignment:pgs. 203-204 #15-17, 29, 30, 34,
35
4.1-4.3 Quiz on Tuesday, October 30th
Algebra 2
