1aprova2n-bat-a-ampmates-matrius-i-determinants.doc - XTEC Blocs

|Nom de l'alumne/a |
|Departament de Matemàtiques IES la | |
|Pineda | |
|Curs 2008/2009 Professor/a: Josep M. | |
|Vigatà | |
|Nivel|2n BAT |Gru|A|Ampl.Matemàtiques| |
|l | |p | | | |
|Dat|6/11/08|Tema de la |Matrius,determ| |
|a | |prova |inants | |
|Referència exàmen: 1a.prova.2n bat a amp.mates. matrius i |
|determinants.doc |
Llegiu bé els enunciats. Si teniu qualsevol dubte, pregunteu-lo en veu
alta. Podeu usar calculadora científica no programable. Feu els exercicis
en l'ordre que millor us vagi. Mireu-vos bé les opcions que hi ha. Heu de
fer l'examen en bolígraf no vermell. Poseu els cognoms i el nom en tots els
fulls. si no heu de fer servir el paper, no el malbarateu.
read well all the headings. if you have any doubt, ask it out aloud. you
can use a non programmable scientific calculator. solve the exercises in
the bes order to you. look welll at all the options. you make not answer in
red ink. write your surnames and your name in all the sheets. |Material |Calculadora |
|recomanable per la |científica |
|prova |no |
| |programable.|
[pic]
You reply THREE of the four questions and you solve ONE of two following
problems. In the
answers, you always explain what is that which you want to make and why.
each question costs 2 points, and the problem, 4 points. You can use
calculator, but calculators or other devices can not be used
that they bring stored information or that can transmit or receive
information.
[pic]
1. Trobar les matrius inverses a les matrius [pic] i [pic] Comprovar que
les matrius trobades són les matrius inverses. Quin rang tenen
cadascuna? Pot aplicar-se indistintament el mètode de GAUSS o bé per
la definició de matriu inversa.
Find the matrices inverse on the matrices and check out that they are the
inverse matrices. Which rank does they have? The method can be applied
GAUSS or for the definition of inverse matrix.
2. Se sap que una matriu no es pot invertir(= no invertible), quan el seu
determinant val zero. Donada la matriu [pic]Quan ha de valer x per a
que la matriu A no sigui invertible?
We know that a matrix is not invertible, when his determining its zero.
Given the matrix A, when its x for that the matrix its not invertible?
3. Donada la matriu [pic], utilitzeu la matriu inversa [pic] per trobar
una matriu X tal que B·X·B = [pic]. Trobar també B2 i B4.
Give the matrix A, you use the inverse matrix for find a matrix X such
that B·X·B=[pic]. Find also B2 and B4. 4. Donades les matrius [pic] i [pic] on a i b són nombres reals, trobeu
els valors de a i b, que fan que les dues matrius commutin, és adir,
que fan que es compleixi A·B =B·A. Give the matrices A and B and where to and b are numbers real, you find the
values of a and a b, that they make both matrices commute, is to suit, that
they make that him fulfill A·B =B·A.
[pic]
1.
a. Siguin les matrius [pic] [pic] i [pic] Trobeu la matriu X que
compleix X= A·(B-C)
b. Donades les matrius [pic] [pic] Trobeu la matriu X que compleix
A·X=B. Calculeu B100 a. A, B, C Are the matrices and Find the matrix X that fulfills X= A·(B-C)
b. Given the matrices you Find the matrix X that fulfills A·X=B. Calculate
B100 2.
a. Donada les matrius [pic] i [pic]utilitzeu la matriu inversa B-1
per a trobar una matriu X tal que B·X·B=D
b. Trobar el determinant[pic]
.
A) Give the matrices and you use the inverse matrix B-1 to find a matrix X
such that B·X·B=D B ) Find the determinant Siguin les matrius [pic] esbrineu si existeix una matriu C que compleixi
B·C=A, i si escau, calculeu-la.
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