1 4 8 -3 -7 -1 2 7 3 4 25. А - -2 2 9. 5 5 6 9 -5 -2 1 4 8 2 0 -1 | 1 4 3.
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![**Matrix and Row Echelon Form**
In this example, we are given a matrix \( A \) and its row echelon form. The original matrix \( A \) is:
\[
A = \begin{bmatrix}
1 & 4 & 8 & -3 & -7 \\
-1 & 2 & 7 & 3 & 4 \\
-2 & 2 & 9 & 5 & 5 \\
3 & 6 & 9 & -5 & -2
\end{bmatrix}
\]
To find the row echelon form of the matrix \( A \), we perform a series of row operations. The result of these operations is:
\[
A \sim \begin{bmatrix}
1 & 4 & 8 & 0 & 5 \\
0 & 2 & 5 & 0 & -1 \\
0 & 0 & 0 & 1 & 4 \\
0 & 0 & 0 & 0 & 0
\end{bmatrix}
\]
### Explanation of the Row Echelon Form:
- The first row of the transformed matrix has a leading 1, which corresponds to the first column.
- The second row is zero except for the second and fifth elements.
- The third row shows that the third column does not contain a leading 1; instead, the leading 1 is in the fourth column.
- The fourth row is entirely zero, indicating that it does not contribute to the rank of the matrix.
### Key Points:
- Each row after the first starts with zeros and then has a leading coefficient of 1 (pivot element) that is to the right of the leading coefficient of the row above it.
- Rows consisting entirely of zeros are at the bottom of the matrix.
- This specific transformation helps in solving systems of linear equations, finding the rank of the matrix, and other linear algebra applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57103f69-f6d8-477a-b236-0336011ee35d%2F6fbcda8a-8217-45a2-b789-84a9a57fe09e%2F1yra7oi_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
