Question

Să se determine matricea: X€M2 (R) astfel încât
(1 2)
(3 5) X=I2​

Answer 1

Răspuns:

Explicație pas cu pas:

$\left(\begin{array}{ccc}1&2\\3&5\\\end{array}\right) \cdot \left(\begin{array}{ccc}a&b\\c&d\\\end{array}\right)=\left(\begin{array}{ccc}1&0\\0&1\\\end{array}\right)$

$\left(\begin{array}{ccc}a+2c&b+2d\\3a+5c&3b+5d\\\end{array}\right)=\left(\begin{array}{ccc}1&0\\0&1\\\end{array}\right)$

a+2c=1    |×3

3a+5c=0

3a+6c=3

3a+5c=0

c=3⇒a=1-6=-5

b+2d=0   |×3

3b+5d=1

3b+6d=0

3b+5d=1

d=-1⇒b=2

$X=\left(\begin{array}{ccc}-5&2\\3&-1\\\end{array}\right)$