Matrix Definition Math Example 2

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Example 2

medium
Write a 3×13 \times 1 column matrix where ai,1=2i−1a_{i,1} = 2i - 1.

Solution

  1. 1
    Step 1: a1,1=2(1)−1=1a_{1,1} = 2(1) - 1 = 1.
  2. 2
    Step 2: a2,1=2(2)−1=3a_{2,1} = 2(2) - 1 = 3.
  3. 3
    Step 3: a3,1=2(3)−1=5a_{3,1} = 2(3) - 1 = 5.
  4. 4
    Result: [135]\begin{bmatrix} 1 \\ 3 \\ 5 \end{bmatrix}

Answer

[135]\begin{bmatrix} 1 \\ 3 \\ 5 \end{bmatrix}
A column matrix (or column vector) has dimensions m×1m \times 1. The formula ai,1=2i−1a_{i,1} = 2i - 1 generates each entry based on its row index.

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

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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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