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Chapter 7: Q7-14E (page 383)

TRUE OR FALSE

14. If A is a noninvertiblen脳nmatrix, then the geometric multiplicity of eigenvalue 0 is n-rank(A).

Short Answer

Expert verified

The given statement, 鈥淚f is a noninvertible nxn matrix, then the geometric multiplicity of eigenvalue 0 isn-rank(A) 鈥� is true.

Step by step solution

01

Define geometric multiplicity

The eigenvalue that is associated with the linearly independent eigenvector is called geometric multiplicity.

02

Find the given statement is true or false

Consider the given statement, 鈥淚f is a noninvertible nxn matrix, then the geometric multiplicity of eigenvalue 0 is n-rank(A).鈥�

Hence, it applies,gemu(0)=dimkerA=n-rankA, where gemu is the geometric multiplicity, and ker is the dimension of the kernel.

Therefore, the given statement is true.

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