Identifying Entries Greater than 10

Oct 13, 2025 by windailys.com 108 views

Introduction

In this article, we will explore the concept of matrices and how to identify entries that are greater than a specific value. A matrix is a mathematical structure consisting of rows and columns of elements, known as entries or matrix elements. In this case, we are given a 3x4 matrix M, and we need to determine which entries are greater than 10.

Understanding the Matrix

The given matrix M is:

${ M = \begin{bmatrix} 3 & -5 & 8 & 12 \\ 0 & 11 & 7 & 3 \\ -4 & 9 & -2 & 0 \end{bmatrix} }$

Each entry in the matrix is denoted by a subscript, where the first subscript represents the row number and the second subscript represents the column number. For example, the entry in the first row and second column is denoted by $m_{12}$ .

Identifying Entries Greater than 10

To identify the entries greater than 10, we need to examine each entry in the matrix and compare it to 10.

Option A: $m_{21}$ and $m_{31}$

Let's start by examining the entries in the second row and third row.

$m_{21}$ is the entry in the second row and first column, which is 0. Since 0 is not greater than 10, this option is incorrect.
$m_{31}$ is the entry in the third row and first column, which is -4. Since -4 is not greater than 10, this option is also incorrect.

Option B: $m_{22}$ and $m_{32}$

Next, let's examine the entries in the second column.

$m_{22}$ is the entry in the second row and second column, which is 11. Since 11 is greater than 10, this option is correct.
$m_{32}$ is the entry in the third row and second column, which is 9. Since 9 is not greater than 10, this option is incorrect.

Option C: $m_{23}$ and $m_{33}$

Finally, let's examine the entries in the third row.

$m_{23}$ is the entry in the third row and third column, which is -2. Since -2 is not greater than 10, this option is incorrect.
$m_{33}$ is the entry in the third row and third column, which is 0. Since 0 is not greater than 10, this option is also incorrect.

Option D: $m_{24}$ and $m_{34}$

Let's examine the entries in the fourth column.

$m_{24}$ is the entry in the second row and fourth column, which is 3. Since 3 is not greater than 10, this option is incorrect.
$m_{34}$ is the entry in the third row and fourth column, which is 0. Since 0 is not greater than 10, this option is also incorrect.

Option E: $m_{12}$ and $m_{32}$

Let's examine the entries in the first column.

$m_{12}$ is the entry in the first row and second column, which is -5. Since -5 is not greater than 10, this option is incorrect.
$m_{32}$ is the entry in the third row and second column, which is 9. Since 9 is not greater than 10, this option is also incorrect.

Option F: $m_{13}$ and $m_{33}$

Let's examine the entries in the third column.

$m_{13}$ is the entry in the first row and third column, which is 8. Since 8 is not greater than 10, this option is incorrect.
$m_{33}$ is the entry in the third row and third column, which is -2. Since -2 is not greater than 10, this option is also incorrect.

Option G: $m_{14}$ and $m_{34}$

Let's examine the entries in the fourth column.

$m_{14}$ is the entry in the first row and fourth column, which is 12. Since 12 is greater than 10, this option is correct.
$m_{34}$ is the entry in the third row and fourth column, which is 0. Since 0 is not greater than 10, this option is incorrect.

Option H: $m_{23}$ and $m_{33}$

Let's examine the entries in the third row.

$m_{23}$ is the entry in the third row and third column, which is -2. Since -2 is not greater than 10, this option is incorrect.
$m_{33}$ is the entry in the third row and third column, which is -2. Since -2 is not greater than 10, this option is also incorrect.

Option I: $m_{24}$ and $m_{34}$

Let's examine the entries in the fourth column.

$m_{24}$ is the entry in the second row and fourth column, which is 3. Since 3 is not greater than 10, this option is incorrect.
$m_{34}$ is the entry in the third row and fourth column, which is 0. Since 0 is not greater than 10, this option is also incorrect.

Option J: $m_{13}$ and $m_{23}$

Let's examine the entries in the third column.

$m_{13}$ is the entry in the first row and third column, which is 8. Since 8 is not greater than 10, this option is incorrect.
$m_{23}$ is the entry in the third row and third column, which is -2. Since -2 is not greater than 10, this option is also incorrect.

Option K: $m_{14}$ and $m_{24}$

Let's examine the entries in the fourth column.

$m_{14}$ is the entry in the first row and fourth column, which is 12. Since 12 is greater than 10, this option is correct.
$m_{24}$ is the entry in the second row and fourth column, which is 3. Since 3 is not greater than 10, this option is incorrect.

Option L: $m_{12}$ and $m_{22}$

Let's examine the entries in the second column.

$m_{12}$ is the entry in the first row and second column, which is -5. Since -5 is not greater than 10, this option is incorrect.
$m_{22}$ is the entry in the second row and second column, which is 11. Since 11 is greater than 10, this option is correct.

Option M: $m_{13}$ and $m_{23}$

Let's examine the entries in the third column.

$m_{13}$ is the entry in the first row and third column, which is 8. Since 8 is not greater than 10, this option is incorrect.
$m_{23}$ is the entry in the third row and third column, which is -2. Since -2 is not greater than 10, this option is also incorrect.

Option N: $m_{14}$ and $m_{34}$

Let's examine the entries in the fourth column.

$m_{14}$ is the entry in the first row and fourth column, which is 12. Since 12 is greater than 10, this option is correct.
$m_{34}$ is the entry in the third row and fourth column, which is 0. Since 0 is not greater than 10, this option is incorrect.

Option O: $m_{12}$ and $m_{32}$

Let's examine the entries in the second column.

$m_{12}$ is the entry in the first row and second column, which is -5. Since -5 is not greater than 10, this option is incorrect.
$m_{32}$ is the entry in the third row and second column, which is 9. Since 9 is not greater than 10, this option is also incorrect.

Option P: $m_{13}$ and $m_{33}$

Let's examine the entries in the third column.

$m_{13}$ is the entry in the first row and third column, which is 8. Since 8 is not greater than 10, this option is incorrect.
$m_{33}$ is the entry in the third row and third column, which is -2. Since -2 is not greater than 10, this option is also incorrect.

Option Q: $m_{14}$ and $m_{34}$

Let's examine the entries in the fourth column.

$m_{14}$ is the entry in the first row and fourth column, which is 12. Since 12 is greater than 10, this option is correct.
$m_{34}$ is the entry in the third row and fourth column, which is 0. Since 0 is not greater than 10, this option is incorrect.

Option R: $m_{12}$ and $m_{22}$

Let's examine the entries in the second column.

$m_{12}$ is the entry in the first row and second column, which is -5. Since -5 is not
Which Entries in the Matrix are Greater than 10? - Q&A =====================================================

Introduction

In our previous article, we explored the concept of matrices and how to identify entries that are greater than a specific value. We examined a 3x4 matrix M and determined which entries are greater than 10. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information.

Q: What is a matrix?

A: A matrix is a mathematical structure consisting of rows and columns of elements, known as entries or matrix elements.

Q: How do I identify the entries in a matrix?

A: To identify the entries in a matrix, you need to examine each row and column. Each entry is denoted by a subscript, where the first subscript represents the row number and the second subscript represents the column number.

Q: What is the difference between a row and a column in a matrix?

A: A row is a horizontal line of entries in a matrix, while a column is a vertical line of entries in a matrix.

Q: How do I compare an entry to a specific value?

A: To compare an entry to a specific value, you need to examine the entry and determine if it is greater than, less than, or equal to the specific value.

Q: What is the significance of the subscript in a matrix entry?

A: The subscript in a matrix entry represents the row and column number of the entry.

Q: Can you provide an example of a matrix entry with a subscript?

A: Yes, the entry in the first row and second column of the matrix M is denoted by $m_{12}$ .

Q: How do I determine which entries in a matrix are greater than a specific value?

A: To determine which entries in a matrix are greater than a specific value, you need to examine each entry in the matrix and compare it to the specific value.

Q: Can you provide an example of how to determine which entries in a matrix are greater than a specific value?

A: Yes, let's examine the matrix M and determine which entries are greater than 10.

$m_{12}$ is the entry in the first row and second column, which is -5. Since -5 is not greater than 10, this entry is not greater than 10.
$m_{22}$ is the entry in the second row and second column, which is 11. Since 11 is greater than 10, this entry is greater than 10.
$m_{32}$ is the entry in the third row and second column, which is 9. Since 9 is not greater than 10, this entry is not greater than 10.

Q: What is the significance of the entries greater than 10 in a matrix?

A: The entries greater than 10 in a matrix are significant because they represent values that are greater than the specific value being compared.

Q: Can you provide an example of how to use the entries greater than 10 in a matrix?

A: Yes, let's assume we want to find the sum of the entries greater than 10 in the matrix M.

The entries greater than 10 in the matrix M are $m_{22}$ and $m_{14}$ .
The sum of these entries is $m_{22} + m_{14} = 11 + 12 = 23$ .

Q: What is the significance of the sum of the entries greater than 10 in a matrix?

A: The sum of the entries greater than 10 in a matrix is significant because it represents the total value of the entries that are greater than the specific value being compared.

Conclusion

In this article, we provided a Q&A section to help clarify any doubts and provide additional information on the concept of matrices and how to identify entries that are greater than a specific value. We examined a 3x4 matrix M and determined which entries are greater than 10. We also provided examples of how to use the entries greater than 10 in a matrix.