IB Mathematics Analysis and Approaches Question Type 2: Finding a Unique Solution to a System of Equations Algebraically Using Matrices or Gaussian Elimination Exercises

Solve the following system of equations:

$$\{\begin{array}{l}7x-5y=1\\ 3x+2y=17\end{array}$$

Solve the triangular system using Gaussian elimination:

$$\{\begin{array}{l}x+2y-z=1\\ y+3z=7\\ 2z=8\end{array}$$

Solve the system using elimination or an augmented matrix:

$$\{\begin{array}{l}4x-y=9\\ 2x+3y=13\end{array}$$

Solve the system by Gaussian elimination:

$$\{\begin{array}{l}x+y+z=6\\ 2x-y+z=3\\ -x+2y+z=7\end{array}$$

Solve the system using Gaussian elimination:

$$\{\begin{array}{l}2x+3y=7\\ 4x-y=5\end{array}$$

Use Gaussian elimination to solve the system and justify uniqueness by noting a nonzero pivot in each column:

$$\{\begin{array}{l}2x+y=5\\ x+3y+z=10\\ y+2z=8\end{array}$$

Solve the system using row-reduction (Gaussian elimination):

$$\{\begin{array}{l}2x+y=5\\ y+3z=10\\ x-z=1\end{array}$$

Use Gaussian elimination to solve:

$$\{\begin{array}{l}3x-y+2z=12\\ 2x+y-z=3\\ x+2y+z=9\end{array}$$

Solve the system using Gaussian elimination:

$$\{\begin{array}{l}1.5x-0.5y=2\\ 0.2x+0.8y=1\end{array}$$

Solve the system using Gaussian elimination:

$$\{\begin{array}{l}0x+2y+z=4\\ x+y+z=6\\ 2x-y+3z=5\end{array}$$