Problems from Computing first-order and second-order determinants

Development:

$$\left|\begin{matrix} 1 & -2\\ 1 & -5 \end{matrix}\right|=1\cdot(-5)-(-2)\cdot1=-5+2=-3$$

Solution:

$$-3$$

Hide solution and development

Development:

$$A=\left(\begin{matrix} 1 & 4 \\ -2 & 3 \end{matrix} \right)$$

The determinant of the $$2\times2$$ matrix is the most immediate:

$$det(A)=\left|\begin{matrix} 1 & 4 \\ -2 & 3 \end{matrix} \right|=1\cdot3-4\cdot(-2)=3+8=11$$

Solution:

$$det(A)=11$$

Hide solution and development