Multiple Choice 5 points Which of these Job Interview questions is Behavioral in nature? Tell me about a time when you had to work with others? What college did you graduate from? Why did you decide to apply for this position? How many years have you worked at your last place of employment?

Use ajdoint matrix to evaluate the inverse of matrix \( A=\left(\begin{array}{cccc}3 & -3 & 2 & 4 \\ -4 & 4 & -2 & -2 \\ 2 & -3 & -3 & -3 \\ -1 & 2 & -4 & -3\end{array}\right) \)

\[ F(x, y, z)=(x-y, z) \] . Determinare la controimmagine di \( (2,2) \) sotto l'azione di \( F \). (i) Determinare una base e la dimensione di Im \( F \) e di Ker \( F \). (ii) Calcolare la dimensione dell'immagine del sottospazio \( U=\mathcal{L}((1,0,0),(0,2,0) \).

Find the rank of matrix A by using the row echelon form. \( A=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 0 & 5\end{array}\right] \)

[The most general such \( R \) is \( U \sqrt{A} \), where \( U \) is some isometry.] 6- Let \( x_{1}, \ldots, x_{n} \) be \( n \) vectors. Let \( G \) be a matrix with elements \( G_{i j}=\left(x_{i}, x_{j}\right) \). Show that \( G \) is a positive matrix. [ \( G \) is called the Gram matrix.]

Let \( T: R^{\wedge} 3 \rightarrow R^{\wedge} 3 \) be a linear transformation such that \( T(1,0,0)=(2,4,-1), T(0,1,0)=(1,3,-2), T(0,0,1)=(0,-2,2) \). Compute \( T(-2,4,-1) \).