Matrices · 2.2.2
Scalar multiplication of a matrix
Scalar multiplication means multiplying every single element of a matrix by the same number, called the scalar. The resulting matrix keeps the same order as the original, and this operation is often combined with addition or subtraction in later, more complex matrix problems.
The official learning standard (2.2.2)
“Multiply a matrix by a number.”
What it means
Scalar multiplication means multiplying every single element of a matrix by the same number, called the scalar. The resulting matrix keeps the same order as the original, and this operation is often combined with addition or subtraction in later, more complex matrix problems.
How it is examined
Paper 1 objective items test direct scalar multiplication of a given matrix. Paper 2 questions often combine scalar multiplication with addition or subtraction, such as finding 2A − 3B, or require solving a matrix equation for an unknown scalar or matrix.
Worked example
Given matrix A = [[3, -1], [0, 4]], find 2A and −3A.
- 2A: multiply every element by 2: [[6, -2], [0, 8]].
- −3A: multiply every element by −3: [[-9, 3], [0, -12]].
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Does scalar multiplication change the order of a matrix?
No, the order stays exactly the same after scalar multiplication. Only the value of each individual element changes, since every element is multiplied by the same number, so a 2×3 matrix remains 2×3 after being multiplied by any scalar.
How is scalar multiplication different from matrix multiplication?
Scalar multiplication multiplies every element by a single ordinary number, while matrix multiplication combines two matrices together using rows and columns with a more complex rule. Scalar multiplication is simpler and always defined, unlike matrix-by-matrix multiplication which needs matching dimensions.
Can I multiply a matrix by a fraction or negative number?
Yes, the scalar can be any real number, including fractions, decimals, or negative numbers. Simply multiply every element in the matrix by that scalar value, following the same rules as multiplying ordinary numbers, and keep track of signs carefully.