All Tasks - Asymptote

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

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.

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?

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, ".".)

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?

Compute the value of the constants, so that the equality is verified: $\begin{bmatrix} 1& 0 &a\\ 0& b &-2 \end{bmatrix}-3 \begin{bmatrix} 2& c &-4\\ 0&\frac{1}{3} &d \end{bmatrix}= \begin{bmatrix} e& 0 &8\\ 0& 2&7 \end{bmatrix}$