Question

va rog, am nevoie urgent ​

Answer 1

Răspuns:

Explicație pas cu pas:

2)

a) det A = 2 · 5 - 3 · (-1) = 10 +3 = 13

b) B = $A^{2}$ - 3A + 2$I_{2}$

B = $\left[\begin{array}{ccc}2&3\\-1&5\\\end{array}\right]$ ·$\left[\begin{array}{ccc}2&3\\-1&5\\\end{array}\right]$ - 3 · $\left[\begin{array}{ccc}2&3\\-1&5\\\end{array}\right]$ + 2 ·$\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right]$

B = $\left[\begin{array}{ccc}-1&-9\\-7&-22\\\end{array}\right]$ -  $\left[\begin{array}{ccc}6&9\\-3&15\\\end{array}\right]$ + $\left[\begin{array}{ccc}2&0\\0&2\\\end{array}\right]$

B = $\left[\begin{array}{ccc}5&-18\\-4&-5\\\end{array}\right]$

c)  X · A = $\left[\begin{array}{ccc}1&1\\-1&1\\\end{array}\right]$

X · $\left[\begin{array}{ccc}2&3\\-1&5\\\end{array}\right]$ = $\left[\begin{array}{ccc}1&1\\-1&1\\\end{array}\right]$

X se scrie ca $\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]$

$\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]$ · $\left[\begin{array}{ccc}2&3\\-1&5\\\end{array}\right]$ = $\left[\begin{array}{ccc}1&1\\-1&1\\\end{array}\right]$

$\left[\begin{array}{ccc}2a-b&3a+5b\\2c-d&3c+5d\\\end{array}\right]$ = $\left[\begin{array}{ccc}1&1\\-1&1\\\end{array}\right]$

2a - b = 1

3a + 5b = 1

2c - d = - 1

3c + 5d = 1

rezolvând sistemul avem a = 6/13, b = -1/13, c = - 4/13 și d = - 5/13