Which Entries In The Following Matrix Are Greater Than 10?$\[ M = \begin{bmatrix} 3 & -5 & 8 & 12 \\ 0 & 11 & 7 & 3 \\ -4 & 9 & -2 & 0 \end{bmatrix} \\]A. \[$ M_{21} \$\] And \[$ M_{31} \$\]B. \[$ M_{22} \$\] And

Feb 28, 2025 by ADMIN 215 views

**Which Entries in the Matrix are Greater than 10?**

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.

Introduction

Understanding the Matrix

Identifying Entries Greater than 10

Option A: m21m_{21}m21​ and m31m_{31}m31​

Option B: m22m_{22}m22​ and m32m_{32}m32​

Option C: m23m_{23}m23​ and m33m_{33}m33​

Option D: m24m_{24}m24​ and m34m_{34}m34​

Option E: m12m_{12}m12​ and m32m_{32}m32​

Option F: m13m_{13}m13​ and m33m_{33}m33​

Option G: m14m_{14}m14​ and m34m_{34}m34​

Option H: m23m_{23}m23​ and m33m_{33}m33​

Option I: m24m_{24}m24​ and m34m_{34}m34​

Option J: m13m_{13}m13​ and m23m_{23}m23​

Option K: m14m_{14}m14​ and m24m_{24}m24​

Option L: m12m_{12}m12​ and m22m_{22}m22​

Option M: m13m_{13}m13​ and m23m_{23}m23​

Option N: m14m_{14}m14​ and m34m_{34}m34​

Option O: m12m_{12}m12​ and m32m_{32}m32​

Option P: m13m_{13}m13​ and m33m_{33}m33​

Option Q: m14m_{14}m14​ and m34m_{34}m34​

Option R: m12m_{12}m12​ and m22m_{22}m22​

Introduction

Q: What is a matrix?

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

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

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

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

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

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

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

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

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

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

Conclusion

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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