Grupa C1

1. Calculati inversa matricei A prin 2 metode:

(1)
\begin{align} A= \begin{pmatrix} 2&3\\ 2&2\\ \end{pmatrix} \end{align}

2.Se considera matricele:

(2)
\begin{align} A= \begin{pmatrix} 3&4\\ 2&3\\ \end{pmatrix}, \qquad B= \begin{pmatrix} 3&4\\ 2&3\\ \end{pmatrix}, \qquad C=A^{-1}+B^2. Calculati \quad C^n. \end{align}

3. Se considera matricele:

(3)
\begin{align} X= \begin{pmatrix} 1\\ 2\\ 3\\ \end{pmatrix}, \qquad Y=\begin{pmatrix} 1\\2\\-3\\ \end{pmatrix}, \qquad, A=XY^t, \qquad B(a)=aA+I_3,a\in \mathbf{R}-\{\frac{1}{4}\} \end{align}

Aratati ca matricea B(a) este inversabila.

4.Se considera matricea:

(4)
\begin{align} A= \begin{pmatrix} 1&-2\\ 2&-3\\ \end{pmatrix}, \qquad Sa\quad se\quad gaseasca\quad matricea\quad B\in \mathbf M_2(R),astfel \quad incat\quad AB=BA=I_2 \end{align}

Radulescu
Dina
Bleiceanu
Simion
Buhulete

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