Solve by using Cramer's Rule: -3x - 4y - 4z = -8 %3D x - 3y - 3z = -19 %3D -x + y – 2z = 3 %3D
Solve by using Cramer's Rule: -3x - 4y - 4z = -8 %3D x - 3y - 3z = -19 %3D -x + y – 2z = 3 %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Solve by using Cramer's Rule:**
\[
\begin{align*}
-3x - 4y - 4z &= -8 \\
x - 3y - 3z &= -19 \\
-x + y - 2z &= 3
\end{align*}
\]
**Instructions for Solving:**
Cramer’s Rule is a straightforward technique to solve a system of linear equations with as many equations as unknowns, provided that the determinant of the coefficient matrix is non-zero. Here, the system of equations consists of three equations with three unknowns: \(x\), \(y\), and \(z\).
1. **Formulate the Coefficient Matrix**:
- Construct the matrix from the coefficients of the variables \(x\), \(y\), and \(z\).
2. **Calculate the Determinant of the Coefficient Matrix**:
- The determinant should be non-zero for Cramer's Rule to apply.
3. **Determine the Determinants for Each Variable**:
- Replace the respective column of the coefficient matrix with the constant terms from the equations and calculate the new determinants.
4. **Apply Cramer’s Rule**:
- Calculate each variable \(x\), \(y\), and \(z\) by dividing the determinant from step 3 by the determinant of the coefficient matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6a59ea6-6b49-4641-82f8-067b1c5942b1%2F92e0227d-b388-42de-87bb-90ab5c34ba45%2Fa8llh6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve by using Cramer's Rule:**
\[
\begin{align*}
-3x - 4y - 4z &= -8 \\
x - 3y - 3z &= -19 \\
-x + y - 2z &= 3
\end{align*}
\]
**Instructions for Solving:**
Cramer’s Rule is a straightforward technique to solve a system of linear equations with as many equations as unknowns, provided that the determinant of the coefficient matrix is non-zero. Here, the system of equations consists of three equations with three unknowns: \(x\), \(y\), and \(z\).
1. **Formulate the Coefficient Matrix**:
- Construct the matrix from the coefficients of the variables \(x\), \(y\), and \(z\).
2. **Calculate the Determinant of the Coefficient Matrix**:
- The determinant should be non-zero for Cramer's Rule to apply.
3. **Determine the Determinants for Each Variable**:
- Replace the respective column of the coefficient matrix with the constant terms from the equations and calculate the new determinants.
4. **Apply Cramer’s Rule**:
- Calculate each variable \(x\), \(y\), and \(z\) by dividing the determinant from step 3 by the determinant of the coefficient matrix.
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