## All Tasks

#### What is the total cost?

João ate a fruit salad that contained x portions of pineapple, y portions of mango and z portions of pear (1 portion is 100g fruit). Matrix A, represents the amounts of energy (calories), iron (mg), and calcium (mg) and Matrix C indicates the prices (euros), of each portion of the 3 fruits. Matrix B shows what João ingested in total. What is the cost of this fruit salad?
$A=\begin{bmatrix}
52&64&39\\
0.5&0.8&0.9\\
18&21&22\\
\end{bmatrix}$ $\begin{array}{l}
calories \\
iron\\
calcium\\
\end{array}$,
$B=\begin{bmatrix}
246 \\3.6\\101\\
\end{bmatrix}$ $\begin{array}{l}
calories \\
iron\\
calcium\\
\end{array}$, $ C=\begin{bmatrix}
0.10\\
0.30\\
0.25\\
\end{bmatrix}$ $\begin{array}{l}
pineapple \\
mango\\
pear\\
\end{array}$

# Matrices

# System of linear equations

Modeling

13

#### Matrices multiplication

Multiply the two matrices and enter the values $a$ to $f$ in the corresponding checkbox.
$\begin{bmatrix}
4 & 2 & 1 \\
0 & -2 & 4 \\
\end{bmatrix}
\cdot
\begin{bmatrix}
1 & 2 & 2 \\
1 & 3 & 3 \\
1 & -1 & 1 \\
\end{bmatrix}
=
\begin{bmatrix}
a & b & c \\
d & e & f \\
\end{bmatrix}$

# Operation

Training

13

#### Matrix add

To illustrate the letter “A” in figures 1 and 2, 20 pixels in a 5×4 grid (for each figure) were used. The color of each pixel can be represented by a specific number, defined by the color scale.
If 1 and 2 can be represented by the matrices $M$ and $N$, determine the matrix $P$ which represents the contrast of the letter “A” when dark gray is changed to light gray and white is changed to black.

# Operation

Modeling

13

#### Total cost (I_M)

A factory, in the production of pieces, has a fixed cost of $8$ euros plus a variable cost of $0.50$ euros per unit produced. If $x$ is the number of pieces produced, what is the cost of $100$ pieces?

# Linear functions

Modeling

9

#### System of linear equations

Given the following matrices $A$ and $B$, find the matrix $X$ such that $AX=B$:
$A=\begin{bmatrix}
0 & 1 & 3 \\
-1 & 2 & 0 \\
1 & -1 & 0
\end{bmatrix}$
$B=\begin{bmatrix}
6 \\ 0 \\ 0
\end{bmatrix}$
(In the answer, fill the spaces that are not entries of the matrix X with a dot, ".".)

# System of linear equations

# Operation

Training

13

#### Chess board modulation

Consider the chess board represented in the figure. Modulating the situation by a numeric matrix, A, in which pawns are represented by the number -1, kings by the number 1, queens by the number 2, rooks by the number 3, and empty spaces with zeros, fill in the blanks of matrix A. What is the dimension of the matrix? If the black queen moves 5 spaces vertically and 3 spaces to the left, what is the position in the matrix of the number representing this piece after the moves?

# Matrices

Modeling

13