For what values of ,x and y are the following matrices equal 7

$straight A equals open square brackets table row cell 2 straight x plus 1 end cell cell 3 straight y end cell row 0 cell straight y squared minus 5 straight y end cell end table close square brackets comma space space straight B equals open square brackets table row cell straight x plus 3 end cell cell straight y squared plus 2 end cell row 0 cell negative 6 end cell end table close square brackets$

Solution

Here
$straight A equals open square brackets table row cell 2 straight x plus 1 end cell cell 3 straight y end cell row 0 cell straight y squared minus 5 straight y end cell end table close square brackets comma space space straight B equals open square brackets table row cell straight x plus 3 end cell cell straight y squared plus 2 end cell row 0 cell negative 6 end cell end table close square brackets$
Now, A = B
$rightwards double arrow space space space space open square brackets table row cell 2 straight x plus 1 end cell cell 3 straight y end cell row 0 cell straight y squared minus 5 straight y end cell end table close square brackets equals open square brackets table row cell straight x plus 3 end cell cell straight y squared plus 2 end cell row 0 cell negative 6 end cell end table close square brackets$

∴ by the definition of equality of matrices.
2 x + 1 = .x + 3, 3 y = + 2 , y² –5 y = – 6
Now 2 x + I = x + 3 ⇒ x= 2
3 x = y² +2 ⇒ y² -3 y + 2 = 0 ⇒ ( y –1) (y – 2) = 0 ⇒ y = I, 2
y²–5 y =-6 ;⇒ -5 y + 6 = 0 ;⇒ (y–2)(y–3) = 0 ;⇒ y = 2.3
Since both the equations 3 y = y² +2 and y² –5 y = – 6 arc to be satisfied
simultaneously, so we have y = 2.
∴A – B when x = 2, y – 2.

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