Matrix Definition Math Example 1

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Example 1

easy
Given A=[3−17052]A = \begin{bmatrix} 3 & -1 & 7 \\ 0 & 5 & 2 \end{bmatrix}, what are the dimensions of AA and what is a2,3a_{2,3}?

Solution

  1. 1
    Step 1: Count rows: 2. Count columns: 3. Dimensions: 2×32 \times 3.
  2. 2
    Step 2: a2,3a_{2,3} means row 2, column 3. That entry is 22.
  3. 3
    Step 3: Verify: row 2 is [0,5,2][0, 5, 2], third element is 22 ✓

Answer

AA is 2×32 \times 3; a2,3=2a_{2,3} = 2
A matrix's dimensions are always given as rows × columns. The notation ai,ja_{i,j} refers to the entry in row ii and column jj.

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 2 medium

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

Example 3 easy

What are the dimensions of [formula]?

Example 4 medium

If [formula] is a [formula] matrix, how many entries does it have? Can you multiply [formula] by a [

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