7.1

Question 1

What is the determinant of these vectors ?

$$\Big\{ \left( \begin{smallmatrix} -1 \\ 2 \\ 2 \\ \end{smallmatrix} \right), \left( \begin{smallmatrix} -2 \\ -2 \\ -2 \\ \end{smallmatrix} \right), \left( \begin{smallmatrix} 0 \\ 0 \\ 0 \\ \end{smallmatrix} \right) \Big\}$$

Question 2

What is the determinant of this matrix ?
$$\begin{pmatrix} 1 & 2 & 2 \\ 1 & 2 & 2 \\ 1 & 3 & 2 \\ \end{pmatrix}$$

Question 3

For what value of $a$ are these vectors linearly dependent ?
$$\Big\{ \left( \begin{smallmatrix} -1 \\ 2 \\ 2 \\ \end{smallmatrix} \right), \left( \begin{smallmatrix} -1 \\ -1 \\ -1 \\ \end{smallmatrix} \right), \left( \begin{smallmatrix} 0 \\ -2 \\ a \\ \end{smallmatrix} \right) \Big\}$$

Question 4

Which matrix has a determinant equal to 5 ?

Question 5

Who first developed the concept of determinant ?