If A=2x+13y0y2−5yand B=x+3y2+20−6 are equal matrices then (x,y)=___

$$A=B$$⇒$$2x+13y0y2$$−$$5y=x+3y2+20$$ −$$6$$⇒$$2x+1=x+3$$⇒$$x=2y2+2=3y$$⇒$$y2$$−$$3y+2=0(y$$−$$1)(y$$−$$2)=0y=1(or)2$$−−−−−−−(i)y2$$−$$5y=$$−$$6y2$$−$$5y+6=0(y$$−$$2)(y$$−$$3)=0y=2(or)3$$−−−−−−−$$(ii)From$$ $$(i) and (ii)∴$$y=2$$∴(x$$,$$y)=(2$$,$$2)

Q.

If $A = [\begin{matrix} 2 x + 1 & 3 y \\ 0 & y^{2} - 5 y \end{matrix}]$ and $B = [\begin{matrix} x + 3 & y^{2} + 2 \\ 0 & - 6 \end{matrix}]$ are equal matrices then $(x, y) =___$

Moderate

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By Expert Faculty of Sri Chaitanya

(1,1)

(2,2)

(0,1)

(2,1)

answer is B.

(Detailed Solution Below)

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Detailed Solution

$\begin{array}{l} A = B \\ \Rightarrow [\begin{matrix} 2 x + 1 & 3 y \\ 0 & y^{2} - 5 y \end{matrix}] = [\begin{matrix} x + 3 & y^{2} + 2 \\ 0 & - 6 \end{matrix}] \\ \Rightarrow 2 x + 1 = x + 3 \Rightarrow x = 2 \\ y^{2} + 2 = 3 y \Rightarrow y^{2} - 3 y + 2 = 0 \\ (y - 1) (y - 2) = 0 \\ y = 1 (o r) 2 - - - - - - - (i) \\ y^{2} - 5 y = - 6 \\ y^{2} - 5 y + 6 = 0 \\ (y - 2) (y - 3) = 0 \\ y = 2 (o r) 3 - - - - - - - (ii) \\ From (i) and (ii) \\ ∴ y = 2 \\ ∴ (x, y) = (2, 2) \end{array}$

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