 #### 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      #### Matrix operations 0

Consider the matrices $$A=\begin{bmatrix} 2&-1\\7&-3\\2&-3 \end{bmatrix},\quad B=\begin{bmatrix} 3&1\\-9&3\\0&0 \end{bmatrix}$$ and $$C=\begin{bmatrix} 1&0&6\\2& -1&0 \end{bmatrix}$$ Compute: $A - 4 B + C^T$

# Operation

Learning
13      #### Triangle of the gradient

The picture shows you different triangles of the gradient for the graph of a proportional function. Complete the sentence.

# Unassigned

Reasoning
8      #### Identification of a matrix

In the table you will find information about group E of the UEFA Champions League 20/21, after the qualifying phase. Considering the data in the table, the matrix, $M$, representative of the results obtained by the 4 teams is given by the elements:

# Matrices

Modeling
13      #### Matrix multiplication

Let $A$ be a $2\times 3$ matrix with elements position $a_{ij}$ given by $a_{ij}=i^2- 2j$ and $B$ be a $3\times 4$ matrix with elements position $b_{ij}$ given by $b_{ij}=(-1)^j(2i-j)$. Let $D=AB$. Find the dimension of $D$ and compute the values $d_{ij}$, for each matrix entry's.

# Operation

Training
13