1
Question
Consider the system of linear equations.
x + 2y + z =1
2x + 3y + z = 2
2x + 2y + 4z =1. The sum of values in solution of (x,y,z) will be __
Consider the system of linear equations.
x + 2y + z =1
2x + 3y + z = 2
2x + 2y + 4z =1. The sum of values in solution of (x,y,z) will be
Open in App
Solution
Here A X=B⎡⎢⎣121231224⎤⎥⎦⎡⎢⎣xyz⎤⎥⎦=⎡⎢⎣121⎤⎥⎦X=A−1.BLet calculate A−1,of⎡⎢⎣121231224⎤⎥⎦|A|=(12−2)−2(8−2)+14−6=10−12−2=−4Cofactor matrix=⎡⎢⎣+10−6−2−62+2−1+1−1⎤⎥⎦Adjoint matrix=⎡⎢⎣+10−6−1−62+1−2+2−1⎤⎥⎦A−1=1−4⎡⎢⎣+10−6−1−621−22−1⎤⎥⎦=⎡⎢
⎢
⎢
⎢⎣−52321432−12−1412−1214⎤⎥
⎥
⎥
⎥⎦X=A−1.B=⎡⎢
⎢
⎢
⎢⎣−5232−1432−12−1412−1214⎤⎥
⎥
⎥
⎥⎦.⎡⎢⎣121⎤⎥⎦=⎡⎢⎣−3−11⎤⎥⎦.Therefore sum of variables willbe−3+−1+1=−3
Here A X=B⎡⎢⎣121231224⎤⎥⎦⎡⎢⎣xyz⎤⎥⎦=⎡⎢⎣121⎤⎥⎦X=A−1.BLet calculate A−1,of⎡⎢⎣121231224⎤⎥⎦|A|=(12−2)−2(8−2)+14−6=10−12−2=−4Cofactor matrix=⎡⎢⎣+10−6−2−62+2−1+1−1⎤⎥⎦Adjoint matrix=⎡⎢⎣+10−6−1−62+1−2+2−1⎤⎥⎦A−1=1−4⎡⎢⎣+10−6−1−621−22−1⎤⎥⎦=⎡⎢ ⎢ ⎢ ⎢⎣−52321432−12−1412−1214⎤⎥ ⎥ ⎥ ⎥⎦X=A−1.B=⎡⎢ ⎢ ⎢ ⎢⎣−5232−1432−12−1412−1214⎤⎥ ⎥ ⎥ ⎥⎦.⎡⎢⎣121⎤⎥⎦=⎡⎢⎣−3−11⎤⎥⎦.Therefore sum of variables willbe−3+−1+1=−3
Suggest Corrections
0
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
