Matrices · 2.2.1
Adding and subtracting matrices
Students add or subtract two matrices by combining corresponding elements in the same row-column position. This operation only works when both matrices share exactly the same order; the resulting matrix keeps that same order, with each element found by adding or subtracting the matching pair.
The official learning standard (2.2.1)
“Add and subtract matrices.”
What it means
Students add or subtract two matrices by combining corresponding elements in the same row-column position. This operation only works when both matrices share exactly the same order; the resulting matrix keeps that same order, with each element found by adding or subtracting the matching pair.
How it is examined
Frequently tested in Paper 1 as direct computation items, and in Paper 2 as part of larger matrix problems that combine addition or subtraction with scalar multiplication, or that require solving a matrix equation for an unknown matrix.
Worked example
Given A = [[4, -2], [3, 5]] and B = [[1, 6], [-2, 0]], find A + B and A − B.
- A + B: add corresponding elements: (4+1, -2+6; 3+(-2), 5+0) = [[5, 4], [1, 5]].
- A − B: subtract corresponding elements: (4-1, -2-6; 3-(-2), 5-0) = [[3, -8], [5, 5]].
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Can I add matrices of different orders?
No, matrix addition and subtraction are only defined when both matrices have exactly the same order. If one matrix is 2×3 and another is 2×2, they cannot be added or subtracted together under any circumstance in the SPM syllabus.
Does the order of subtraction matter?
Yes, A − B is not the same as B − A for matrices, just like in ordinary numbers. Subtracting in the wrong order reverses the sign of every element in the answer, so always follow the order given in the question exactly.
How do I add matrices with negative numbers?
Add corresponding elements using normal integer rules, being careful with signs, for example, 3 + (−5) = −2. Work through each position systematically, one pair of corresponding elements at a time, to avoid sign errors when matrices contain negative values.