Question

Exercitiul 2=punct B

Answer 1

Răspuns:

Explicație pas cu pas:

a. $\left|\begin{array}{ccc}1&1\\2&1\\\end{array}\right|=1-2=-1$

b. $\left(\begin{array}{ccc}1&1\\2&2\\\end{array}\right) \cdot \left(\begin{array}{ccc}1&a\\b&1\\\end{array}\right) =\left(\begin{array}{ccc}1+b&1+a\\2+2b&2a+2\\\end{array}\right)$

$\left|\begin{array}{ccc}1+b&1+a\\2+2b&2a+2\\\end{array}\right|=$

(1+b)2(a+1)-(1+a)2(1+b)=0

c. $\left(\begin{array}{ccc}1+b&1+a\\2+2b&2a+2\\\end{array}\right)=\left(\begin{array}{ccc}1+2a&1+2a\\2+b&b+2\\\end{array}\right)$

1+b=1+2a

b=2a

1+a=1+2a

a=2a

a=0

b=0

2. x°y=|x-y|+1

a. 3°5=|3-5|+1=2+1=3

b. a-b=?

a=(2°3)°4=2°4=3

b=2°(3°4)=2°2=1

a-b=3-1=2

c. m°n=m

|m-n|+1=m

caz 1 m>n

m-n+1=m

n=1

caz 2 m<n

n-m+1=m

n+1=2m

exista o infinitate de solutii naturale, n impar