#### 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
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#### 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
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#### 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