Use Cramer's Rule to solve (if possible) the system of linear equations. If not possible, enter IMPOSSIBLE 4x1- X2 + x3 = -7 2x1 + 2x2 + 3x3 = 14 5x₁2x2 + 6x3 = +80
Use Cramer's Rule to solve (if possible) the system of linear equations. If not possible, enter IMPOSSIBLE 4x1- X2 + x3 = -7 2x1 + 2x2 + 3x3 = 14 5x₁2x2 + 6x3 = +80
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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![### Solving Systems of Linear Equations Using Cramer's Rule
**Problem:**
Use Cramer's Rule to solve (if possible) the system of linear equations shown below. If not possible, enter IMPOSSIBLE.
\[
\begin{align*}
4x_1 - x_2 + x_3 &= -7 \\
2x_1 + 2x_2 + 3x_3 &= 14 \\
5x_1 - 2x_2 + 6x_3 &= 8
\end{align*}
\]
**Instructions:**
1. **Identify the coefficients matrix (A):**
Coefficients of \(x_1\), \(x_2\), and \(x_3\) from the system of equations.
\[
A = \begin{pmatrix}
4 & -1 & 1 \\
2 & 2 & 3 \\
5 & -2 & 6
\end{pmatrix}
\]
2. **Compute the determinant of matrix A (\(\det(A)\)):**
\[
\det(A) = 4 \begin{vmatrix}
2 & 3 \\
-2 & 6
\end{vmatrix}
-(-1) \begin{vmatrix}
2 & 3 \\
5 & 6
\end{vmatrix}
+ 1 \begin{vmatrix}
2 & 2 \\
5 & -2
\end{vmatrix}
\]
3. **Determinants of the 2x2 matrices:**
\[
\begin{vmatrix}
2 & 3 \\
-2 & 6
\end{vmatrix} = (2 * 6 - 3 * (-2)) = 12 + 6 = 18
\]
\[
\begin{vmatrix}
2 & 3 \\
5 & 6
\end{vmatrix} = (2 * 6 - 3 * 5) = 12 - 15 = -3
\]
\[
\begin{vmatrix}
2 & 2 \\
5 & -2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e1fa912-5e0c-4d6e-bcb6-bc3942e62084%2Fd353eba8-977c-4f9f-8dbe-128e634178ea%2Fme1b0z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Systems of Linear Equations Using Cramer's Rule
**Problem:**
Use Cramer's Rule to solve (if possible) the system of linear equations shown below. If not possible, enter IMPOSSIBLE.
\[
\begin{align*}
4x_1 - x_2 + x_3 &= -7 \\
2x_1 + 2x_2 + 3x_3 &= 14 \\
5x_1 - 2x_2 + 6x_3 &= 8
\end{align*}
\]
**Instructions:**
1. **Identify the coefficients matrix (A):**
Coefficients of \(x_1\), \(x_2\), and \(x_3\) from the system of equations.
\[
A = \begin{pmatrix}
4 & -1 & 1 \\
2 & 2 & 3 \\
5 & -2 & 6
\end{pmatrix}
\]
2. **Compute the determinant of matrix A (\(\det(A)\)):**
\[
\det(A) = 4 \begin{vmatrix}
2 & 3 \\
-2 & 6
\end{vmatrix}
-(-1) \begin{vmatrix}
2 & 3 \\
5 & 6
\end{vmatrix}
+ 1 \begin{vmatrix}
2 & 2 \\
5 & -2
\end{vmatrix}
\]
3. **Determinants of the 2x2 matrices:**
\[
\begin{vmatrix}
2 & 3 \\
-2 & 6
\end{vmatrix} = (2 * 6 - 3 * (-2)) = 12 + 6 = 18
\]
\[
\begin{vmatrix}
2 & 3 \\
5 & 6
\end{vmatrix} = (2 * 6 - 3 * 5) = 12 - 15 = -3
\]
\[
\begin{vmatrix}
2 & 2 \\
5 & -2
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