If  A=102−1and B=3142 a matrices C such that  2A+3B+2Cis a null matrix then ___

# If  $A=\left[\begin{array}{cc}1& 0\\ 2& -1\end{array}\right]$and $B=\left[\begin{array}{cc}3& 1\\ 4& 2\end{array}\right]$ a matrices C such that  $2A+3B+2C$is a null matrix then ___

1. A

$\frac{1}{2}\left[\begin{array}{cc}11& 3\\ 8& 4\end{array}\right]$

2. B

$\frac{1}{2}\left[\begin{array}{cc}-11& -3\\ -16& -8\end{array}\right]$

3. C

$\frac{1}{2}\left[\begin{array}{cc}11& 3\\ 16& 8\end{array}\right]$

4. D

$\left[\begin{array}{cc}-11& -3\\ -16& -8\end{array}\right]$

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

$\begin{array}{l}2A+3B+2C=0\\ ⇒2C=-2A-3B\\ =-2\left[\begin{array}{cc}1& 0\\ 2& -1\end{array}\right]-3\left[\begin{array}{cc}3& 1\\ 4& 2\end{array}\right]\\ =\left[\begin{array}{cc}-2-9& 0-3\\ -1-12& 2-6\end{array}\right]\\ =\left[\begin{array}{cc}-11& -3\\ -16& -8\end{array}\right]\\ c=\left[\begin{array}{cc}-\frac{11}{2}& -\frac{3}{2}\\ -8& -4\end{array}\right]\end{array}$  +91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)