Question

Jr. Inter :: MATHEMATICS - 1 27 Find the rank of the matrix [1. 1 1 1 1 1 . 1 1 1] [1 1 11 det A - 1(1 - 1).- 1 (1 - 11

JEE/Engineering Exams

Maths

Solution

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It is a 2 atep thetuod (1) Stepl Find the dituminat of ( 3 times 3 ) matrix st it is non zero then rowe is 3 qfit is zeno then go to styp ( (2) leq+infty 2 ) Tate any ( 2 x 2 ) sub mater x and find its dureminant If it is non zero then vante is 2 If it is zero then rente is 1 * In this case nutrix is ( left.int begin{array}{l}11 11 111end{array}right] ) wing atef 1 Jho detininat of wathix is 2080 as all Nowd and colven in are some so going to ( rightarrow+infty ) Now in att 2 vabing a ( 2 x 2 ) and matrix QS all the swo matrix an aame ( left[begin{array}{ll}1 & 1end{array}right] ) and deten minant of ( left[begin{array}{lll}11 & 1 & 11 & 2end{array}right) 0 ) 2000 as all Now ound rolwmn an tand Hence the rawe of matix is I Rane af Marix ( left[begin{array}{l}111 111 111end{array}right]=1 )