Home › JEE Advanced › Algebra › In a non-zero matrix $A$, the rank $r$ means that
In a non-zero matrix $A$, the rank $r$ means that
Aevery minor of order $r$ is zero
Bthere exists at least one non-zero minor of order $r$, and every minor of order greater than $r$ is zero
Call minors of every order are non-zero
Dthe determinant of $A$ is non-zero
Answer & Solution
Correct answer: B. there exists at least one non-zero minor of order $r$, and every minor of order greater than $r$ is zero
The rank is the highest order of a non-zero minor. So at least one minor of order $r$ must be non-zero, while all minors of order greater than $r$ must vanish. That is exactly option B.
Related questions
Simplifying an equation, a student reaches a statement that can never be true. The equatioAfter squaring both sides of a radical equation, a student finds a root that fails the oriSolving such an equation, a student clears every denominator at once by multiplying througAn equation contains at least one rational expression, with a variable in a denominator. TTo clear a complex number from a denominator, a student multiplies by the term found by flComplex numbers cannot sit on an ordinary number line, so they are plotted on a plane whosRather than drawing a number line, a student writes the solution set with brackets and parA statement joins two inequalities together in one line, such as 2 < x < 7. That statement