All Tasks

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.
 
# Proportionality

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

Invertible matrices

Consider the matices $A$ and $B$: $A=\begin{bmatrix} 2 & -4 \\ -1 & 2 \\ \end{bmatrix}$ $B=\begin{bmatrix} 2 & -4 \\ -1 & -2 \\ \end{bmatrix}$. Which of the following is true?
# Inverse
# Determinate

Training
13