Linear Algebra **Problem 7**: Use an adjoint matrix to solve the linear system.\[\begin{aligned}&2x + 3y - 5z = 22 \\&y + 3z = -8 \\&2z = -6 \\\end{aligned}\]**Explanation:**This problem requires solving a system of linear equations using the adjoint matrix method. The system consists of three equations with three variables: $x$, $y$, and $z$.1. **Equation 1:** $2x + 3y - 5z = 22$2. **Equation 2:** $y + 3z = -8$3. **Equation 3:** $2z = -6$To solve the system, organize it into matrix form as:\[ A \cdot \mathbf{x} = \mathbf{b} \]where $A$ is the coefficient matrix, $\mathbf{x}$ is the column matrix of variables, and $\mathbf{b}$ is the column matrix of constants. The adjoint method involves calculating the inverse of $A$ using its adjoint for finding $\mathbf{x}$.

The given system of linear equation is 2x+3y+5z=22, y+3z=-8 and 2z=-6. Express the above system of…

Answered: 7. Use an adjoint matrix to solve the…

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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Linear Algebra

**Problem 7**: Use an adjoint matrix to solve the linear system.

\[
\begin{aligned}
&2x + 3y - 5z = 22 \\
&y + 3z = -8 \\
&2z = -6 \\
\end{aligned}
\]

**Explanation:**

This problem requires solving a system of linear equations using the adjoint matrix method. The system consists of three equations with three variables: $x$, $y$, and $z$.

1. **Equation 1:** $2x + 3y - 5z = 22$
2. **Equation 2:** $y + 3z = -8$
3. **Equation 3:** $2z = -6$

To solve the system, organize it into matrix form as:

\[ A \cdot \mathbf{x} = \mathbf{b} \]

where $A$ is the coefficient matrix, $\mathbf{x}$ is the column matrix of variables, and $\mathbf{b}$ is the column matrix of constants. The adjoint method involves calculating the inverse of $A$ using its adjoint for finding $\mathbf{x}$.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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