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Maths-

General

Easy

Question

if $open square brackets table row 1 2 3 row 3 1 2 row 2 3 1 end table close square brackets$ $open square brackets table row x row y row z end table close square brackets$ = $open square brackets table row cell 4 – 2 end cell row cell 0 – 6 end cell row cell – 12 end cell end table close square brackets$ $open square brackets table row 2 row 1 end table close square brackets$ then (x, y, z) is equal to -

(–4, 2, 2)
(4, 2, 2)
(–4, –2, –2)
(4, –2, –2)

The correct answer is: (–4, 2, 2)

$open square brackets table row cell x plus 2 y plus 3 z end cell row cell 3 x plus y plus 2 z end cell row cell 2 x plus 3 y plus z end cell end table close square brackets$ = $open square brackets table row cell 8 – 2 end cell row cell 0 – 6 end cell row cell – 2 plus 2 end cell end table close square brackets$
$rightwards double arrow$ x + 2y + 3z = 6 …(1)
$rightwards double arrow$ 3x + y + 2z = – 6…(2)
2x + 3y + z = 0…(3)
Solving equation (1), (2), (3) we get
x = – 4, y = 2, z = 2.

Related Questions to study

If A = $open square brackets table row 1 cell 1 divided by 2 end cell row 0 1 end table close square brackets$ then A⁶⁴ is :

If A = $open square brackets table row 1 cell 1 divided by 2 end cell row 0 1 end table close square brackets$ then A⁶⁴ is :

Which of the following is not a disproportionation reaction?
I) $NH subscript 4 NO subscript 3 not stretchy rightwards arrow with straight capital delta on top straight N subscript 2 straight O plus straight H subscript 2 straight O$
II) $straight P subscript 4 not stretchy rightwards arrow with straight capital delta on top PH subscript 3 plus HPO subscript 2 superscript ⊖$
III) $PCl subscript 5 not stretchy rightwards arrow with straight capital delta on top PCl subscript 3 plus Cl subscript 2$
IV) $IO subscript 3 superscript ⊖ plus straight I to the power of ⊖ not stretchy ⟶ straight I subscript 2$

Which of the following is not a disproportionation reaction?
I) $NH subscript 4 NO subscript 3 not stretchy rightwards arrow with straight capital delta on top straight N subscript 2 straight O plus straight H subscript 2 straight O$
II) $straight P subscript 4 not stretchy rightwards arrow with straight capital delta on top PH subscript 3 plus HPO subscript 2 superscript ⊖$
III) $PCl subscript 5 not stretchy rightwards arrow with straight capital delta on top PCl subscript 3 plus Cl subscript 2$
IV) $IO subscript 3 superscript ⊖ plus straight I to the power of ⊖ not stretchy ⟶ straight I subscript 2$

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