Question

Let matrices $A=\left[\begin{array}{ccc}2x+1& 3y& \\ 0& y^2-5y& \end{array}\right],B=\left[\begin{array}{ccc}x+3& y^2+2& \\ 0& -6& \end{array}\right]$ are equal, then which of the following is(are) not correct

• A. $x=2,y=-2$
• B. $x=-2,y=2$
• C. $x=1,y=1$
• D. $x=2,y=2$

Answer 1

Answer: (A), (B), (C)

$x=1,y=1$

Given, $\left[\begin{array}{ccc}2x+1& 3y& \\ 0& y^2-5y& \end{array}\right]=\left[\begin{array}{ccc}x+3& y^2+2& \\ 0& -6& \end{array}\right]$
On comaring like elements, we get
$2x+1=x+3$
$\Rightarrow x=2$
$3y=y^2+2$
$\Rightarrow y^2-3y+2=0$
$\Rightarrow (y-1)(y-2)=0$
$\Rightarrow y=1,2\cdots \left(i\right)$
and $y^2-5y=-6$
$\Rightarrow y^2-5y+6=0$
$\Rightarrow (y-2)(y-3)=0$
$\Rightarrow y=2,3\cdots \left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$ we get
$y=2$
$\therefore x=2,y=2$