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University Business Math Matrices and Input-Output Models — Unit Notes

Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 7 definitions and 7 theorems, 6 worked examples, 1 diagram, in 17 printable pages. This page lists what the notes cover. The notes themselves come with the University Business Math bundle.

Unit notes — in the bundle

17 pages 14 definitions & theorems 6 worked examples 38 key words 6 Try-it pairs, answered 14-row at-a-glance table 38-entry glossary Fill-in-the-blank guided twin 1 diagram Letter size, print-ready

Not sold separately. The practice worksheet for this unit is free, with no email and no account.

Matrices and Input-Output Models — what the notes cover

7 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.

What you need

Also in this section: 1 note on method and common errors.

Modelling a business problem as a linear system

  • Definition — Linear equations and systems

Also in this section: 1 worked example, 1 note on method and common errors.

Augmented matrices and row operations

  • Definition — Matrices and the augmented matrix of a system
  • Theorem — The three row operations

Also in this section: 1 worked example, 1 note on method and common errors.

Gauss-Jordan elimination and the three outcomes

  • Definition — Reduced row echelon form
  • Theorem — Gauss-Jordan elimination
  • Theorem — The three outcomes of a linear system

Also in this section: 1 worked example, 1 note on method and common errors.

Matrix sums, scalar multiples and products

  • Definition — Sums, differences and scalar multiples
  • Definition — The matrix product
  • Theorem — What matrix algebra keeps and what it loses

Also in this section: 1 worked example, 1 note on method and common errors.

The inverse matrix and matrix equations

  • Definition — Identity matrix and inverse
  • Theorem — Finding an inverse by row reduction
  • Theorem — Matrix equations

Also in this section: 1 worked example, 1 note on method and common errors.

Input-output models

  • Definition — Technology matrix, total output and final demand
  • Theorem — Solving an input-output model

Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.

Where the notes are

The notes are one of the documents in the University Business Math Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Matrices and Input-Output Models practice worksheet is free and stays free.

Best value for the whole year

Every University Business Math topic — the complete Solutions Bundle

One download, one payment, the whole program. For all 9 University Business Math units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.

9 units · 36 PDFs · 190 pages$24.99
  • Worked solutions, not answer lists — every step written out
  • Covers the whole year's program at this level
  • Less than the price of one hour of tutoring — for the entire year's solutions
Everything paid, in one file $24.99CAD · one payment University Business Math bundle — coming soon Not on sale yet

Practise it, then test yourself

Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.

Matrices and Input-Output Models practice worksheet   About the Matrices and Input-Output Models unit test

← All 9 University Business Math unit notes

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