Simulic
English

Matrices – types, sum, scalar multiple, transpose and matrix product

MathematicsAlgebraAges 16–17

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Use with my class

Set the order m × n and the entries of two matrices A and B, see which types A belongs to (row, column, square, zero, diagonal, scalar, identity, triangular, symmetric, skew-symmetric), test A = B, work out A + B, A − B, kA and the transpose, and split a square matrix into its symmetric and skew-symmetric parts. The product screen checks the orders and builds AB row by column, with real-data examples on sales and nutrition.

Lesson: Matrices and matrix operations

What it shows

A matrix is a rectangular array of numbers with m rows and n columns, called an m × n matrix; aᵢⱼ is the entry in row i and column j. This simulation lets you build two matrices of any order up to 4 × 4 and see which special types they are, when they are equal, and how sums, differences, scalar multiples and transposes are formed entry by entry. Every square matrix splits into a symmetric part and a skew-symmetric part. The product AB exists only when A has as many columns as B has rows, and each entry is a row of A times a column of B.

How to use

Tap a cell of A or B and drag sideways, or use the Entry slider, to change it; use the − and + buttons to change the numbers of rows and columns. On Types, tap a type to load an example or press New task. On Sum and scalar, choose the Operation. On Transpose, press Transpose. On Product, press Run or Step, or press Question and type the entry.

Parameters you can change

  • Screen Types of matrix, Sum and scalar, Transpose, Product
  • Example Starter, Two matrices of the same order, Two square matrices, Sales: quantities and prices, Nutrition: servings
  • Matrix A (rows separated by ;)
  • Matrix B (rows separated by ;)
  • Matrix shown (Types, Transpose) A, B
  • Operation A + B, A − B, kA, A = B ?
  • Scalar k -3–3
  • Currency (sales example) From the language, US dollar, Euro, Indian rupee, Indonesian rupiah, Saudi riyal

Questions to explore

  1. Why can a 2 × 3 matrix be multiplied by a 3 × 4 matrix but not the other way round?
  2. Which entries of a skew-symmetric matrix must be zero, and why?
  3. Can AB and BA both exist and still be different?

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