Question

if A is a matrix of order 3x3 such that |A|=4 and B is another matrix of the same order such that B=A^3, find |B|

Answer 1

calculate the present age of Ankur and Aryan , at 1st we have to set up equation as per the given clue in the question. Then solve the equation to find out the age of Ankur and Aryan.

\sf\small\underline{Given\:in\:case-(i):-}

Givenincase−(i):−

\tt{:\implies Ankur\:age\:: Aryan\:age=1:2}:⟹Ankurage:Aryanage=1:2

\tt{:\implies x:y=1:2}:⟹x:y=1:2

\tt{:\implies 2x=y-------(i)}:⟹2x=y−−−−−−−(i)

\sf\small\underline{Given\:in\:case-(i):-}

Givenincase−(i):−

\tt{:\implies After\:3\: years\:_{(Ankur\:age: Aryan\:age)}=3:5}:⟹After3years

(Ankurage:Aryanage)

=3:5

\tt{:\implies (x+3):(y+3)=3:5}:⟹(x+3):(y+3)=3:5

\tt{:\implies 5(x+3)=3(y+3)}:⟹5(x+3)=3(y+3)

\tt{:\implies 5x+15=3y+9}:⟹5x+15=3y+9

\tt{:\implies 5x-3y=9-15}:⟹5x−3y=9−15

\tt{:\implies 5x-3y=-6----(ii)}:⟹5x−3y=−6−−−−(ii)

Substitutes the value y in eq (ii)

\tt{:\implies 5x - 3(2x)=-6}:⟹5x−3(2x)=−6

\tt{:\implies 5x-6x=-6}:⟹5x−6x=−6

\tt{:\implies -x=-6}:⟹−x=−6

\tt{:\implies x=6}:⟹x=6

Putting the value of x in eq (ii)

\tt{:\implies 5x-3y=-6}:⟹5x−3y=−6

\tt{:\implies 5(6)-3y=-6}:⟹5(6)−3y=−6

\tt{:\implies 30-3y=-6}:⟹30−3y=−6

\tt{:\implies -3y=-6-30}:⟹−3y=−6−30

\tt{:\implies 3y=36}:⟹3y=36

\tt{:\implies y=12}:⟹y=12

\sf\large{Hence,}Hence,

\tt\blue{:\implies The\: present\:age\:_{(Ankur)}=6\: years}:⟹Thepresentage

(Ankur)

=6years

\tt\green{:\implies The\: present\:age\:_{(Aryan)}=12\: years}:⟹Thepresentage

(Aryan)

=12years