Learn with Amar
Teaching video
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Browse grades and teaching videos01 · Read and understand
What you will learn
- Build matrices with labelled dimensions.
- Compute row-by-column products.
- Interpret every output entry in context.
Before you start
Multiply and add whole numbers; read a table by its row and column labels.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Kit A contains 2 pens and 1 folder; Kit B contains 1 pen and 3 folders. Class 1 orders 4 A and 2 B kits. Class 2 orders 1 A and 3 B kits. Find each class's supply totals.
Why this math matters
A matrix organizes related calculations. Matrix multiplication combines counts with per-unit requirements. Labels matter as much as arithmetic: the shared dimension must represent the same categories in the same order.
Set up the model
A useful answer starts with clear assumptions:
- Kit contents are fixed, with no substitutions.
- Orders use whole kits, and the kit order is A then B in both input tables.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Turn several kit orders into a supply list with matrices
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Kit A contains 2 pens and 1 folder; Kit B contains 1 pen and 3 folders. Class 1 orders 4 A and 2 B kits. Class 2 orders 1 A and 3 B kits. Find each class's supply totals.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Organize the two tables
O = [[4, 2], [1, 3]]; S = [[2, 1], [1, 3]]
O has class rows and kit columns. S has kit rows and supply columns ordered pens, then folders. The matching kit dimension connects them.
Compute the first class's row
pens = 4(2) + 2(1) = 10; folders = 4(1) + 2(3) = 10
Each output combines one order row with one supply column. Add requirements from both kit types.
Complete and interpret the product
OS = [[10, 10], [5, 10]]
Class two needs 1(2) + 3(1) = 5 pens and 1(1) + 3(3) = 10 folders. Output rows remain classes and columns remain supplies.
The result
Class 1 needs 10 pens and 10 folders; Class 2 needs 5 pens and 10 folders.
Although both inputs happen to be 2 × 2, reversing them would not preserve their labelled meaning. Matrix multiplication is generally order-sensitive, and numerical dimensions alone do not establish a useful model.
Common mistakes to catch
- Entry-by-entry multiplication misses the required sums over kit types.
- Reordering kit columns without reordering the matching kit rows changes the calculation.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
A new class orders 2 A kits and 1 B kit. Find its supply row.
Show a hint
Multiply [2, 1] by the same supply matrix.
Reveal answer and explanation
[5, 5]: 5 pens and 5 folders
Pens: 2(2) + 1(1) = 5. Folders: 2(1) + 1(3) = 5.
Practice 2
If every original order doubles, how does the output matrix change?
Show a hint
Every term in each row-by-column sum doubles.
Reveal answer and explanation
[[20, 20], [10, 20]]
The new product is 2(OS), so every supply total doubles. Kit contents themselves have not changed.
Take the idea with you
Label matrix rows and columns before computing. The inner labels should match, while the outer labels describe the output.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Rotate a point using the imaginary unit
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