#### Calculating coordinates

Calculate the x-coordinate of the point P(x; -3) on the graph of a proportional function with f(x) = - 1.5x

# Proportionality

Training
8

#### Gaussian Elimination and Matrix Inverse

Find the inverse of a matrix $A = \begin{bmatrix} 2&1& 1\\-1&0&-{1 \over 2}\\0&0&1\end{bmatrix}$ using Gauss – Jordan Method (write the matrix using decimal numbers).
# Inverse
#

Training
13

#### Invertible matrices

Consider the matices $A$ and $B$: $A=\begin{bmatrix} 5 & 3 \\ 6 & 4 \\ \end{bmatrix}$ $B=\begin{bmatrix} 5 & -10 \\ -2 & 4 \\ \end{bmatrix}$. Which of the following is true?
# Inverse
# Determinate

Training
13

#### Matrix resolution of a Cramer's System

The solution of the system $\begin{cases} 2x+y+z=1 \\ 2y-z=1 \\ 3x+z=1 \end{cases}$ is: (in the resolution use the matrix equation $AX = B$ and the inverse matrix of $A$)
# System of linear equations
# Equations

Learning
13

#### Electric circuits and system of linear equations

Compute the currents in the electrical circuit shown in the figure.

# System of linear equations

Modeling
13

#### SLE as a matrix equation

A system of linear equations can be represented as the matrix equation $A X = B$. Consider the system of linear equations $$\left\{ \begin{array}{l} 2x+3y+2z=1\\ x+4y-z=0\\ 5x+z=9 \end{array} \right.$$ The matrices $A$, $X$ and $B$ of the system are:
# Equations
# System of linear equations

Training
13