1
Question
If ⎡⎢⎣2−110−34⎤⎥⎦A=⎡⎢⎣−1−8−101−2−592215⎤⎥⎦, then sum of all the elements of matrix A is
If ⎡⎢⎣2−110−34⎤⎥⎦A=⎡⎢⎣−1−8−101−2−592215⎤⎥⎦, then sum of all the elements of matrix A is
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Solution
The correct option is B 1
⎡⎢⎣2−110−34⎤⎥⎦A=⎡⎢⎣−1−8−101−2−592215⎤⎥⎦
let A=[abcdef]
⇒⎡⎢⎣2−110−34⎤⎥⎦[abcdef]=⎡⎢⎣−1−8−101−2−592215⎤⎥⎦
⇒⎡⎢⎣2a−d2b−e2c−fabc−3a+4d−3b+4e−3c+4f⎤⎥⎦=⎡⎢⎣−1−8−101−2−592215⎤⎥⎦
⇒2a−d=−1,2b−e=−8,2c−f=−10 -----(1)
and a=1,b=−2,c=−5 ----(2)
from (1) and (2)
a+b+c=−6 and d+e+f=7
∴ Sum of all the elements in the matrix a+b+c+d+e+f=1
Hence, option B.
⎡⎢⎣2−110−34⎤⎥⎦A=⎡⎢⎣−1−8−101−2−592215⎤⎥⎦
let A=[abcdef]
⇒⎡⎢⎣2−110−34⎤⎥⎦[abcdef]=⎡⎢⎣−1−8−101−2−592215⎤⎥⎦
⇒⎡⎢⎣2a−d2b−e2c−fabc−3a+4d−3b+4e−3c+4f⎤⎥⎦=⎡⎢⎣−1−8−101−2−592215⎤⎥⎦
⇒2a−d=−1,2b−e=−8,2c−f=−10 -----(1)
and a=1,b=−2,c=−5 ----(2)
from (1) and (2)
a+b+c=−6 and d+e+f=7
∴ Sum of all the elements in the matrix a+b+c+d+e+f=1
Hence, option B.
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