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Chapter 3: Q2E (page 163)

IfA is a5脳6matrix of rank4, then the nullity ofAis1.

Short Answer

Expert verified

The given statement is false. If A is a 5脳6matrix of rank 4, then the nullity of A is 2.

Step by step solution

01

Concept used

According to the rank-nullity theorem, for anymatrixA, the equation

(nullity ofA) + (rank ofA)= m

holds true. This theorem is also known as the fundamental theorem of linear algebra.

02

Given data

Given a matrixAwhich is a5脳6 matrix of rank 4.

03

Applying the concept

In accordance with the rank-nullity theorem, the following equation holds true for the given matrixA

(nullity ofA) + (rank ofA)= m

From the given data, it can be briefed out that (rank ofA)=4and the value ofmturns out be6as the given matrix is of the order5脳6.

Therefore, by substituting the values in the above equation, we get

(nullity of A)=6-4=2

04

Result

Therefore, it will be wrong to say that if A is a 5脳6matrix of rank 4, then the nullity of A is 1.

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