Ever wondered how a shop keeps track of many orders at once?
Ada buys 2 mudu of rice and 3 of beans; Tunde buys 4 of rice and 1 of beans. Put the orders in a table of numbers — a matrix — and one multiplication gives both bills at once.
Revision notes
Add, subtract, scale and multiply matrices — and see why AB is usually not the same as BA.
Ada buys 2 mudu of rice and 3 of beans; Tunde buys 4 of rice and 1 of beans. Put the orders in a table of numbers — a matrix — and one multiplication gives both bills at once.
A matrix is a rectangle of numbers in rows and columns. Its order is rows × columns, so 2513 is 2 × 2.
You can add or subtract matrices of the same order by adding or subtracting matching entries.
To multiply by a number (a scalar), multiply every entry: 3 × 2−104 = 6−3012.
🔑 Key idea: Add or subtract matching entries; a scalar multiplies every entry.
Each entry of AB comes from a row of A times a column of B: multiply the pairs and add.
1234 × 56: row 1 gives 1 × 5 + 2 × 6 = 17 and row 2 gives 3 × 5 + 4 × 6 = 39, so the answer is 1739.
AB exists only when the columns of A = rows of B. A (2 × 3) times B (3 × 1) gives a 2 × 1 matrix: the outer numbers give the order.
🔑 Key idea: (m × n) × (n × p) = (m × p). Inner numbers must match.
For numbers 3 × 5 = 5 × 3, but for matrices AB is usually not equal to BA, so keep the order the question gives.
The identity matrix I = 1001 acts like the number 1: AI = IA = A.
🔑 Key idea: Usually AB ≠ BA.
A = −1−331 and B = −2341. Find AB.
Step 1: Row × column for each entry
Row 1 × column 1: (−1) × (−2) + (−3) × 4 = −10
Row 1 × column 2: (−1) × 3 + (−3) × 1 = −6
Row 2 × column 1: 3 × (−2) + 1 × 4 = −2
Row 2 × column 2: 3 × 3 + 1 × 1 = 10
Step 2: Answer
AB = −10−6−210
Answer: −10−6−210
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