Suppose that an eigenvalue of matrix A is zero. Prove that A must therefore be singular.
1 answer:
Eigenvalue:
In a linear system of equations, eigenvalues are actually special set of scalars which are associated with these equations.
Singular Matrix:
A matrix whose determinant is Zero is called singular matrix.
Step-by-step explanation:
.
If Matrix A is singular it means that
det (A) = 0
det (A-0.I)=0
because
So,
det (A-0.I) = 0 implies that 0 is eigenvalue of matrix A.
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