Matrices
A matrix question in 11+ non-verbal reasoning shows a grid of figures, usually 2 by 2 or 3 by 3, where one rule links the figures along each row and a second rule links the figures down each column. One cell, usually the bottom-right, is left blank, and the pupil must combine both rules to work out the missing figure.
Method
- Read across the top row first and work out the single rule that changes the first figure into the next.
- Read down the first column and work out the single rule that changes the top figure into the lower figures.
- Check that the row rule also works for the other rows, and the column rule also works for the other columns.
- Apply the row rule and the column rule together to build up the missing cell feature by feature.
- Treat a 3 by 3 grid as a single reading-order sequence, like a Series question, if the usual row and column rules do not fit.
- Compare your built-up answer to the options and choose the one that matches every feature, not just one.
Worked example
A 2 by 2 grid of shapes is described below. Top-left: a small white triangle. Top-right: a small black triangle. Bottom-left: a large white triangle. What does the bottom-right cell look like?
- Compare top-left to top-right: the shading changes from white to black, while size and shape stay the same. That is the row rule.
- Compare top-left to bottom-left: the size changes from small to large, while shading and shape stay the same. That is the column rule.
- Apply the row rule (shading becomes black) to the bottom-left figure, giving a large black triangle.
- Check this also matches applying the column rule (size becomes large) to the top-right figure, which gives the same result.
- Final answer: The bottom-right cell is a large black triangle.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Top-left: circle with 3 dots. Top-right: circle with 5 dots. Bottom-left: circle with 3 dots. What is the bottom-right cell, and what rule did you use?
A 3 by 3 grid of shapes is described below. Row 1: pentagon rotated 0 degrees, hexagon rotated 0 degrees, heptagon rotated 0 degrees. Row 2: pentagon rotated 90 degrees clockwise, hexagon rotated 90 degrees clockwise, heptagon rotated 90 degrees clockwise. Row 3: pentagon rotated 180 degrees clockwise, hexagon rotated 180 degrees clockwise, ? Find the missing cell.
A 3 by 3 grid of shapes is described below. The shape is fixed by column: column 1 is always a triangle, column 2 is always a square, column 3 is always a pentagon. The shading is fixed by row: row 1 unshaded, row 2 grey, row 3 solid black. The dot count is fixed by row: row 1 has 0 dots, row 2 has 1 dot, row 3 has 2 dots. Find the bottom-right cell (row 3, column 3).
Free printable worksheet
Want more practice on paper? Download the matrices worksheet pack - 28 pages of exam-style questions with a full mark scheme. No sign-up, no email wall - just the PDF, free for personal and classroom use.
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