Question

Calculate the value for each determinant:​

Answer 1

Answer:

Please check the explanation.

Step-by-step explanation:

• Find the matrix determinant according to the formula:

       $\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc$

1)

$\det \begin{pmatrix}3&-1\\ \:-3&4\end{pmatrix}$

$=3\cdot \:4-\left(-1\right)\left(-3\right)$

$=9$

2)

$\det \begin{pmatrix}-12&-1\\ 12&5\end{pmatrix}$

$=\left(-12\right)\cdot \:5-\left(-1\right)\cdot \:12$

$=-48$

3)

$\det \begin{pmatrix}0&-1\\ \:\:\:17&4\end{pmatrix}$

$=0\cdot \:4-\left(-1\right)\cdot \:17$

$=17$

4)

$\det \begin{pmatrix}8&-1\\ \:\:\:-4&-1\end{pmatrix}$

$=8\left(-1\right)-\left(-1\right)\left(-4\right)$

$=-12$

5)

$\det \begin{pmatrix}2&-1\\ 2&-1\end{pmatrix}$

$=2\left(-1\right)-\left(-1\right)\cdot \:2$

$=0$

6)

$\det \begin{pmatrix}1&0\\ \:\:0&1\end{pmatrix}$

$=1\cdot \:1-0\cdot \:0$

$=1$