Matrices
Scalar multiplication
Multiplying every element of a matrix by the same number.
| English | Scalar multiplication |
|---|---|
| Bahasa Melayu | Pendaraban skalar |
| 中文 | 标量乘法 |
How it is used
Multiplying the matrix (2 −1; 0 4) by the scalar 3 multiplies every element by 3: 3 × (2 −1; 0 4) = (6 −3; 0 12).
Where it shows up in SPM
In the Matrices chapter (Form 5), often combined with addition, such as 2A − B. Paper 1 tests a quick scalar multiply; in Paper 2 it turns up inside longer expressions and when writing an inverse as a fraction times a matrix.
Don't confuse it with
Frequently asked questions
Do I multiply only the first number by the scalar?
No. Every single element in the matrix is multiplied by the scalar, not just one.
For 2 × (3 5; −1 0) you get (6 10; −2 0). Missing an element, especially a 0 or a negative one, is a common mistake that loses marks.
What happens to negative elements when I use a scalar?
The usual sign rules apply to each element. A positive scalar keeps signs, so 3 × (−2) = −6.
A negative scalar flips them, so −2 × (−3 1) = (6 −2). Handle each element's sign separately as you multiply.