Matrix Definition Math Example 4

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Example 4

medium
If AA is a 4×34 \times 3 matrix, how many entries does it have? Can you multiply AA by a 3×53 \times 5 matrix?

Solution

  1. 1
    Entries: 4×3=124 \times 3 = 12.
  2. 2
    Multiplication ABAB: inner dimensions must match. AA is 4×34 \times \mathbf{3} and BB is 3×5\mathbf{3} \times 5. Yes, result is 4×54 \times 5.

Answer

12 entries; yes, result is 4×54 \times 5
A matrix has m×nm \times n total entries. For multiplication ABAB, the number of columns of AA must equal the number of rows of BB. The result has dimensions (rows of AA) × (columns of BB).

About Matrix Definition

A matrix is a rectangular array of numbers arranged in rows (horizontal) and columns (vertical). An m×nm \times n matrix has mm rows and nn columns. Each number in the matrix is called an entry or element, identified by its row and column position.

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More Matrix Definition Examples

Example 1 easy

Given [formula], what are the dimensions of [formula] and what is [formula]?

Example 2 medium

Write a [formula] column matrix where [formula].

Example 3 easy

What are the dimensions of [formula]?

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