## All Tasks

#### 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

# Determinant

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

#### Matrix equation 0.2

Let $A$, $B$, $C$ and $X$ be matrices with real values, and suppose that all the matrices involved have an inverse and the operations involved are all possible. Solve in order of $X$ the following matrix equation:
$( X A +B )^T = C$

# Equations

Learning

13

#### Matrix equation 0.1

Let $A$, $B$, and $X$ be matrices with real values, and suppose that all the matrices involved have an inverse and the operations involved are all possible. Solve in order of $X$ the following matrix equation:
$A X = B$

# Equations

Learning

13