Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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how would i solve this with the x-
![**Solve the Matrix Equation**
The problem involves a matrix equation which is given by:
\[ x - \begin{bmatrix} 2 & -8 \\ -4 & 2 \end{bmatrix} = \begin{bmatrix} 4 & -6 \\ 2 & -8 \end{bmatrix} \]
To solve this equation, we need to find matrix \( x \).
**Explanation:**
1. **Matrix on the Left-Hand Side**: The left-hand side of the equation consists of an unknown matrix \( x \) minus a known 2x2 matrix \(\begin{bmatrix} 2 & -8 \\ -4 & 2 \end{bmatrix}\).
2. **Matrix on the Right-Hand Side**: This is a known 2x2 matrix \(\begin{bmatrix} 4 & -6 \\ 2 & -8 \end{bmatrix}\).
**Solution Approach**:
To isolate \( x \), add the matrix \(\begin{bmatrix} 2 & -8 \\ -4 & 2 \end{bmatrix}\) to both sides of the equation. This will give you:
\[ x = \begin{bmatrix} 4 & -6 \\ 2 & -8 \end{bmatrix} + \begin{bmatrix} 2 & -8 \\ -4 & 2 \end{bmatrix} \]
3. **Matrix Addition**:
- Add corresponding elements of the two matrices.
\[
x = \begin{bmatrix} 4+2 & -6+(-8) \\ 2+(-4) & -8+2 \end{bmatrix}
\]
4. **Result**:
- Calculate each element:
\[
x = \begin{bmatrix} 6 & -14 \\ -2 & -6 \end{bmatrix}
\]
Therefore, matrix \( x \) is \(\begin{bmatrix} 6 & -14 \\ -2 & -6 \end{bmatrix}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4068a1aa-9e6d-4ad8-b018-87550c835fe0%2Fbeb15600-437f-44ec-a9ac-4f1759104aca%2Fxqfw0s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve the Matrix Equation**
The problem involves a matrix equation which is given by:
\[ x - \begin{bmatrix} 2 & -8 \\ -4 & 2 \end{bmatrix} = \begin{bmatrix} 4 & -6 \\ 2 & -8 \end{bmatrix} \]
To solve this equation, we need to find matrix \( x \).
**Explanation:**
1. **Matrix on the Left-Hand Side**: The left-hand side of the equation consists of an unknown matrix \( x \) minus a known 2x2 matrix \(\begin{bmatrix} 2 & -8 \\ -4 & 2 \end{bmatrix}\).
2. **Matrix on the Right-Hand Side**: This is a known 2x2 matrix \(\begin{bmatrix} 4 & -6 \\ 2 & -8 \end{bmatrix}\).
**Solution Approach**:
To isolate \( x \), add the matrix \(\begin{bmatrix} 2 & -8 \\ -4 & 2 \end{bmatrix}\) to both sides of the equation. This will give you:
\[ x = \begin{bmatrix} 4 & -6 \\ 2 & -8 \end{bmatrix} + \begin{bmatrix} 2 & -8 \\ -4 & 2 \end{bmatrix} \]
3. **Matrix Addition**:
- Add corresponding elements of the two matrices.
\[
x = \begin{bmatrix} 4+2 & -6+(-8) \\ 2+(-4) & -8+2 \end{bmatrix}
\]
4. **Result**:
- Calculate each element:
\[
x = \begin{bmatrix} 6 & -14 \\ -2 & -6 \end{bmatrix}
\]
Therefore, matrix \( x \) is \(\begin{bmatrix} 6 & -14 \\ -2 & -6 \end{bmatrix}\).
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