Matrices
A matrix is a rectangular arrangement of entries. Its order is rows × columns. Add equal-order matrices entry by entry. For multiplication, the first matrix's column count must equal the second's row count; each output entry is a row–column dot product.
What this guide covers
Displaying and interpreting matrix data, scalar multiplication, addition and compatible matrix products. No determinants or inverses are needed here.
Syllabus reference: 2026 Mathematics 4052, N9, page 8. These are Mentora search groupings, not new official syllabus categories.
The content in this guide was also checked against 2027 G3 Mathematics K310, N9, page 8 on 2026-09-12. This is subject-content alignment, not a claim of complete syllabus coverage.
Worked example
A sales matrix M has rows Monday and Tuesday and columns notebooks and pens: M = [[2, 3], [4, 1]]. Prices are P = [[5], [2]] dollars. Find MP and interpret it.
M is 2 × 2 and P is 2 × 1, so MP is 2 × 1. Monday revenue = 2 × 5 + 3 × 2 = $16. Tuesday revenue = 4 × 5 + 1 × 2 = $22. Thus MP = [[16], [22]]. Rows retain the day labels, and the output unit is dollars, not items.
Try three practice checks
Attempt each on paper before revealing the worked answer. These sample particular skills; they do not diagnose the whole topic or establish mastery.
Check 1
A is 2 × 3 and B is 3 × 4. State the order of AB and whether BA is defined.
Show worked answer
The inner counts 3 match, so AB is 2 × 4. BA would require 4 = 2, which is false, so BA is not defined.
Check 2
If A = [[1, 2], [3, 4]] and B = [[5, 0], [−1, 2]], find 2A + B.
Show worked answer
First 2A = [[2, 4], [6, 8]]. Add matching entries to get [[7, 4], [5, 10]].
Check 3
Compute [[1, 2], [0, 3]] × [[4], [5]].
Show worked answer
The first row gives 1 × 4 + 2 × 5 = 14; the second gives 0 × 4 + 3 × 5 = 15. The product is the column [[14], [15]].
Mistakes to watch for
- Write rows before columns when stating order.
- A product is not entry-by-entry multiplication; each result uses a whole row and column.
- AB and BA need not both exist or be equal. Check dimensions and preserve labels and units.
If one of these occurs, compare the relevant step with the worked example, then try a different question before drawing conclusions.
Useful foundations to check
These connections suggest what may help with this skill. Selecting a topic says nothing about your current attainment.
Applications and next topics
Matrices organise repeated calculations such as revenue for several days. Before a contextual product, check that a row's quantities correspond to the prices in the column in the same order.
Choose a useful next resource
To understand a recurring error rather than relearn the whole skill: Organise contextual multi-step solutions.
Sources and review
Original Mentora public practice, authored for this guide. Worked answers and syllabus mapping checked during editorial QA on 2026-09-12; no independent expert review is claimed. Graph connections are Mentora learning hints, not an official SEAB sequence. Read the source and examination-year notes.