#### 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