Question

2. If one of the eigen value of a matrix A is zero, then the matrix A is
a. Singular
b. Non-singular
c. Orthogonal
d. None of these
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Answer 1

Answer:

If one of the eigenvalues of a square matrix a order 3×3 is zero, then prove that det A=0. Now if one of the eigenvalues is zero, one root of λ should be zero. Therefore, constant term in the above polynominal is zero.

Step-by-step explanation:

hope it helps of not then sorry

Answer 2

Answer:

Option (a) singular matrix is correct.

Step-by-step explanation:

We know that to find eigen values, we use | A - $\lambda$ I | = 0

where A is the given matrix

          $\lambda$  is the eigen values

   and I is the identity matrix

Given that one of the eigen values is 0

This means that  $\lambda$  = 0 will satisfy the above equation.

=> | A - 0 * I | = 0

=> | A - 0 | = 0

=> | A | = 0

As | A | = 0 , it is singular matrix

Therefore, Option (a) is correct.