## All Tasks

#### 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
$$A=\begin{bmatrix}
0&1&1&1\\1& 0&1&1\\1&1&0&1\\1&1&1&0
\end{bmatrix}$$
Knowing that 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.

# Proportionality

Reasoning

8