AP EAMCET20225 Jul 2022Evening ShiftMathematicsMatricesActual
If the rank of the matrix A= [ array cccc 1 & 2 & 1 & -1 -1 & 2 & 3 & 5 0 & 1 & k & k array ] is 2 and k is a real number, then k is a root of the following quadratic equation
Options
- Ax^2+3 x+2=0
- Bx^2+x-2=0
- Cx^2+x-6=0
- Dx^2-x-6=0
Correct answer
B. x^2+x-2=0
Step-by-step solution
A= [ array cccc 1 & 2 & 1 & -1 -1 & 2 & 3 & 5 0 & 1 & k & k array ] Given, rank of A =2 there must be 2 rows | columns which are linearly dependent. using Echelon transformation, R ₂ R ₂+ R ₁A= [ array cccc 1 & 2 & 1 & -1 0 & 4 & 4 & 4 0 & 1 & k & k array ] Clearly at k=1, R ₂ and R ₃ will be identical. Which will make rank =2 Taking k=1 out of given options k=1 only. satisfies x^2+x-2=0