SECTION - I Given A=\left[\begin{array}{cc}2 & -6 \ 2 & 0]\end{array}, B=\left[\begin{array}{cc}-3 & 2 \ 4 & 0]\end{array}, C=\left[\begin{array}{cc}4 & 0 \ 0 & 2]\end{array} . Find the matrix X such that A+2 X=2 B+ C.

ICSE Class X Math 2013 Solved Paper - Question 1

Question : 1 of 46

Marks: +1, -0

SECTION - I

Given

A={[\table 2 , -6 ; 2 , 0]}, B={[\table -3 , 2 ; 4 , 0]},

C={[\table 4 , 0 ; 0 , 2]}

.
Find the matrix

X

such that

A+2 X=2 B+

Solution:

Given

A={[\table 2 , -6 ; 2 , 0]}, B={[\table -3 , 2 ; 4 , 0]},

C={[\table 4 , 0 ; 0 , 2]}

∵ \;\; A+2 X=2 B+C

Putting the given values, we get

{{[\table 2 , -6 ; 2 , 0 ]}+2 {\X} }\;=2{[\table -3 , 2 ; 4 , 0 ]}

+{[\table 4 , 0 ; 0 , 2 ]}

2 {\X}\;={[\table -6+4 , 4+0 ; 8+0 , 0+2 ]}

-{[\table 2 , -6 ; 2 , 0 ]}

{\X}\;=\;{1}/{2}{[\table -4 , 10 ; 6 , 2 ]}

{\X}\;={[\table -2 , 5 ; 3 , 1 ]}

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