Question

Calculate the value for each determinant:​

Answer 1

Please check the explanation.

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`