7. Systems of Equations & Matrices

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}w + x - y + z = -2 \\2w - x + 2y - z = 7 \\-w + 2x + y + 2z = -1\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}x + y - 2z = 2 \\3x - y - 6z = -7\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}x + 2y + 3z = 5 \\y - 5z = 0\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}2x + y - z = 2 \\3x + 3y - 2z = 3\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}w - 3x + y - 4z = 4 \\-2w + x + 2y = -2 \\3w - 2x + y - 6z = 2 \\-w + 3x + 2y - z = -6\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}2w + x - y = 3 \\w - 3x + 2y = -4 \\3w + x - 3y + z = 1 \\w + 2x - 4y - z = -2\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}w - 2x - y - 3z = -9 \\w + x - y = 0 \\3w + 4x + z = 6 \\2x - 2y + z = 3\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}8x + 5y + 11z = 30 \\-x - 4y + 2z = 3 \\2x - y + 5z = 12\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}3x + 4y + 2z = 3 \\4x - 2y - 8z = -4 \\x + y - z = 3\end{cases}$

In Exercises 1 - 24, use Gaussian Elimination to find the complete solution to each system of equations, or show that none exists. $\begin{cases}5x + 12y + z = 10 \\2x + 5y + 2z = -1 \\x + 2y - 3z = 5\end{cases}$

In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists.

In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists.

In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists.

Find the following matrices: $A+B$

$A = \begin{bmatrix}2 \\-4 \\1\end{bmatrix}, B = \begin{bmatrix}-5 \\3 \\-1\end{bmatrix}$

a. Give the order of each matrix.

b. If A = [aᵢⱼ] , identify a₃₂ and a₂₃, or explain why identification is not possible.

$\begin{bmatrix}1 & -5 & \pi & e \\0 & 7 & -6 & -\pi \\-2 & \frac{1}{2} & 11 & -\frac{1}{5}\end{bmatrix}$