#### 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

#### Power of a matrix 1

Consider the identity matrix $I_4$ and the matrix $$A=\begin{bmatrix} 0&1&1&1\\1& 0&1&1\\1&1&0&1\\1&1&1&0 \end{bmatrix}$$ Matrix $A^2$ is a linear combination of matrices A and $I_4$, ie, $\exists x,y\in R: A^2 = x A + y I_4$ Which of the following statements is true?

# Operation

Reasoning
13

#### Matrices multiplication 0

Let $A=\begin{bmatrix} 4&-2&5\\2&6&0\\3&3&3\end{bmatrix}$ and $B=\begin{bmatrix} 1&0&0\\0&2&-3\\6&-6&2\end{bmatrix}$ be real matrices $M_{3\times 3}$. The matrix $AB$ is:

# Operation

Training
13