If A=\left[\begin{array}{cc}3 & x \ 0 & 1]\end{array} and B=\left[\begin{array}{cc}9 & 16 \ 0 & -y]\end{array}, find x and y when {\A}^2= {\B}.

ICSE Class X Math 2015 Solved Paper - Question 5

Question : 5 of 52

Marks: +1, -0

A={[\table 3 , x ; 0 , 1]}

and

B={[\table 9 , 16 ; 0 , -y]}

, find

x

and

y

when

{\A}^2= {\B}

Solution:

\;\;\text " Given : "\; {\A}={[\table 3 , x ; 0 , 1 ]} \;\text " and "\; {\B}={[\table 9 , 16 ; 0 , -y ]}

\; {\A}^2= {\B}

\;{{[\table 3 , x ; 0 , 1 ]}{[\table 3 , x ; 0 , 1 ]} }

={[\table 9 , 16 ; 0 , -y ]}

\;{{[\table 3 × 3+x × 0 , 3 × x+x × 1 ; 0 × 3+1 × 0 , 0 × x+1 × 1 ]} ={[\table 9 , 16 ; 0 , -y ]} }

\;{{[\table 9 , 4 x ; 0 , 1 ]} }={[\table 9 , 16 ; 0 , -y ]}

By equality of matrices,

4 x\;=16\;\;\text " and "\;\;1\;=-y

x\;=4\;\;\text " and "\;\;y\;=-1

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