One card is drawn at random from a pack of playing cards. What is the probability that it is: i) A King? ii) A red card? iii) A picture card? (A picture card is a King, Queen or Jack) iv) Not a picture card?

2. Use Theorem 4.2 .1 to determine which of the following are subspaces of \( M_{n n} \). (a) The set of all diagonal \( n \times n \) matrices. (b) The set of all \( n \times n \) matrices \( A \) such that \( \operatorname{det}(A)=0 \). (c) The set of all \( n \times n \) matrices \( A \) such that \( \operatorname{tr}(A)=0 \). (d) The set of all symmetric \( n \times n \) matrices. (e) The set of all \( n \times n \) matrices \( A \) such that \( A^{T}=-A \). (f) The set of all \( n \times n \) matrices \( A \) for which \( A \mathbf{x}=0 \) has only the trivial solution. (g) The set of all \( n \times n \) matrices \( A \) such that \( A B=B A \) for some fixed \( n \times n \) matrix \( B \).

a) when \( v=4 \) and \( w=1 \), the expression is equal to b) when \( v=6 \) and \( w=2 \), the expression is equal to

3) Hullar intervalo (s) solvein de la inecoucion dada. \( \quad \) Seno: a) \( 2 x-3(x-1)+4(x+2) \leq 3 x+2(3 x-2) \)

2- Enic dit : « Le tanif moyen sur cette seance etait de \( 7,125 € \). " Lucie lui repond: « Pas du tout, tu devrais refaire ton calcul. " Qui a raison? Donner en detaillant le calcul, le tanif moyen de cette seance.

Dada la función \( f(x)=x^{2}+4 x+5 \) determinar: a) Concavidad b) Eje simetría c) Intersección eje y d) Intersección con el eje \( x \) o ceros de la función e) Vértice de la parábola. f) Grafique la función