Which of the following is not a possible ordered pair for a matrix with 6 elements

General
1

which of the following is not a possible ordered pair for a matrix with 6 elements.

2

Which of the following is not a possible ordered pair for a matrix with 6 elements?

Answer:

When dealing with matrices, an “ordered pair” typically refers to the dimensions of the matrix, specifically the number of rows and columns. To determine which ordered pairs are possible for a matrix with 6 elements, we need to consider various configurations where the product of the number of rows and columns equals 6. Possible dimensions (ordered pairs) that satisfy this condition include:

  1. (1 \times 6)
  2. (6 \times 1)
  3. (2 \times 3)
  4. (3 \times 2)

Let’s break it down:

  • (1 \times 6): This denotes a matrix with 1 row and 6 columns, making a total of (1 \times 6 = 6) elements.
  • (6 \times 1): This configuration has 6 rows and 1 column, also totaling (6 \times 1 = 6) elements.
  • (2 \times 3): This signifies a matrix with 2 rows and 3 columns, giving (2 \times 3 = 6) elements.
  • (3 \times 2): This indicates a matrix with 3 rows and 2 columns, amounting to (3 \times 2 = 6) elements.

Ordered pairs that do not result in 6 elements include any configuration where the product of the dimensions does not equal 6. For example:

  • (2 \times 2) and (3 \times 3):
    • (2 \times 2): This yields 4 elements ((2 \times 2 = 4)).
    • (3 \times 3): This yields 9 elements ((3 \times 3 = 9)).

Hence, both these configurations are examples of ordered pairs that cannot form a matrix with exactly 6 elements. If asked to choose from a given list, any dimensions not included in the solutions above (such as (2 \times 2) or (3 \times 3)) would be correct options for “not a possible ordered pair” for a matrix with 6 elements.

If further examples or clarifications are needed, feel free to ask!