spain-selectividad 2019 Q1

spain-selectividad · Other · selectividad__madrid_matematicas-II_ordinaria 2.5 marks Matrices Determinant and Rank Computation
Given the matrices $A = \left( \begin{array} { c c c c } 1 & 3 & 4 & 1 \\ 1 & a & 2 & 2 - a \\ - 1 & 2 & a & a - 2 \end{array} \right)$ and $M = \left( \begin{array} { c c c } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1 \end{array} \right)$; find: a) ( 1.5 points) Study the rank of A as a function of the real parameter a. b) ( 1 point) Calculate, if possible, the inverse of the matrix AM for the case a $= 0$. 
Given the matrices $A = \left( \begin{array} { c c c c } 1 & 3 & 4 & 1 \\ 1 & a & 2 & 2 - a \\ - 1 & 2 & a & a - 2 \end{array} \right)$ and $M = \left( \begin{array} { c c c } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1 \end{array} \right)$; find:
a) ( 1.5 points) Study the rank of A as a function of the real parameter a.
b) ( 1 point) Calculate, if possible, the inverse of the matrix AM for the case a $= 0$.
Paper Questions
Q1 Q2 Q3 Q4