Students will learn that a scalar is a single number that can scale each value in a matrix. They will practice multiplying matrices by scalars and performing scalar addition and subtraction of matrices. For a matrix A and scalar c, the scalar product cA means multiplying each element of A by c. Examples show multiplying matrices by scalars like 2A and -1/2A, and adding or subtracting matrices with scalar coefficients like 5C - B.

2. Learning Intention and Success
Criteria
 Learning Intention: Students will understand that a
scalar is a single number which can scale each value in
a matrix
 Success Criteria: You will be able to multiply a matrix
of any order by a scalar and perform matrix addition
and subtraction with scalars involved

3. Scalar Multiplication Definition
For example, if
𝐴 =
1 2 3
4 5 6
Then
2𝐴 =
1 × 2 2 × 2 3 × 2
4 × 2 5 × 2 6 × 2
2𝐴 =
2 4 6
8 10 12
 For a matrix 𝐴 and a scalar number 𝑐, the scalar
product 𝑐𝐴 means to multiply each element of 𝐴 by
the value of 𝑐.

4. Scalar Multiplication Examples
Ex 1: Evaluate
a) 3
0 4
−7 2
=
3 × 0 3 × 4
3 × −7 3 × 2
=
0 12
−21 6
b) −
1
2
8 −6
0 5
=
−4 3
0 −
5
2

5. Scalar Multiplication Examples
Ex2: Let 𝐴 =
1 0 2
−2 3 1
, 𝐵 =
3 4
7 −1
−2 0
and 𝐶 =
1 0
0 1
1 1
Evaluate each of the following, if possible.
a) 2𝐴
b) 5𝐶 − 𝐵
c) 𝐵 − 2𝐴 𝑇
d) 𝐵 + 2𝐴

6. Scalar Multiplication Examples
Ex2: Let 𝐴 =
1 0 2
−2 3 1
, 𝐵 =
3 4
7 −1
−2 0
and 𝐶 =
1 0
0 1
1 1
Evaluate each of the following, if possible.
a) 2𝐴
= 2
1 0 2
−2 3 1
=
2 0 4
−4 6 2

7. Scalar Multiplication Examples
Ex2: Let 𝐴 =
1 0 2
−2 3 1
, 𝐵 =
3 4
7 −1
−2 0
and 𝐶 =
1 0
0 1
1 1
Evaluate each of the following, if possible.
b) 5𝐶 − 𝐵
= 5
1 0
0 1
1 1
−
3 4
7 −1
−2 0
=
5 0
0 5
5 5
−
3 4
7 −1
−2 0
=
2 −4
−7 6
7 5

8. Scalar Multiplication Examples
Ex2: Let 𝐴 =
1 0 2
−2 3 1
, 𝐵 =
3 4
7 −1
−2 0
and 𝐶 =
1 0
0 1
1 1
Evaluate each of the following, if possible.
c) 𝐵 − 2𝐴 𝑇
=
3 4
7 −1
−2 0
− 2
1 0 2
−2 3 1
T
=
3 4
7 −1
−2 0
− 2
1 −2
0 3
2 1
=
3 4
7 −1
−2 0
−
2 −4
0 6
4 2
=
1 8
7 −7
−6 −2

9. Scalar Multiplication Examples
Ex2: Let 𝐴 =
1 0 2
−2 3 1
, 𝐵 =
3 4
7 −1
−2 0
and 𝐶 =
1 0
0 1
1 1
Evaluate each of the following, if possible.
d) 𝐵 + 2𝐴
=
3 4
7 −1
−2 0
+ 2
1 0 2
−2 3 1
𝑁𝑜𝑡 𝑐𝑜𝑚𝑝𝑎𝑡𝑖𝑏𝑙𝑒 − 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛