Download 4.1 Matrix Operations

4.1 Matrix Operations
Algebra 2
Definition
 Matrix-A rectangular arrangement of numbers in rows and
columns
 Dimensions- number of rows then columns
 Entries- The numbers
 Equal Matrices- their dimensions are the same and the
entries in corresponding positions are equal.
Example
1)
Determine the dimensions of the following matrices
1)
5 3
−2 1
2)
2 .5 4
Examples
2)
Tell whether the following matrices are equal or not equal
1)
5
2
−1
2.5 −1
and
1
−0.2 3
−
3
5
2)
1 2
0 −1
and
3 5
8 3
Adding and Subtracting
 To add or subtract matrices, add or subtract corresponding
entries.
 Note: you can only add or subtract matrices if they have the
same dimensions
Examples
3) Perform the indicated operation, if possible.
1)
0
1
4 + −9
3
8
2)
3 3
1 3
−
9 −5
4 −8
Examples
4)
Perform the indicated operation, if possible.
1 3
4 −8
1)
9 −7 +
2)
7 8
1 0
+
−9 0
1 3
Definition
 Scalar- A real number
 Scalar Multiplication- multiplying a number by a real number
 To multiply a matrix by a scalar (scalar multiplication):
multiply each entry in the matrix by the scalar
Examples
5) Perform the indicated operation.
1) 6
2 −3
8 4
2) 4 3
−2
7
Examples
6)
Perform the indicated operations
4 −7
3 6
1) −1 3
3 + 9 −8
2 −9
1 −4
2) 2
6
6
−2
1 −5
−
3
7 5
Solving Matrix Equations
7)
Solve the matrix equation for x and y
1) 4
8 0
4 −2𝑥
+
− 2𝑦
1
6
=
2) 3
10 2
𝑥
−
5 4𝑦
−1
0 −9
=
18 21
5
1
48 −48
0
8
Properties of Matrix Operations
 Associative Property of Addition:
𝐴+𝐵 +𝐶 =𝐴+ 𝐵+𝐶
 Commutative Property of Addition:
𝐴+𝐵 =𝐵+𝐴
 Distributive Property of Addition:
𝑐 𝐴 + 𝐵 = 𝑐𝐴 + 𝑐𝐵
 Distributive Property of Subtraction:
𝑐 𝐴 − 𝐵 = 𝑐𝐴 − 𝑐𝐵