If the rank of the matrix [(λ,-1,0),(0,λ,-1),(-1,0,λ)] is 2, then λ is …… (a) 1 (b) 2 (c) 3 (d) any real number

Question

If the rank of the matrix \(\begin{bmatrix} λ&-1&0 \\[0.3em] 0&λ&-1 \\-1&0&λ \\[0.3em] \end{bmatrix}\) is 2, then λ is …… 

(a) 1 

(b) 2 

(c) 3 

(d) any real number

Answer 1

(a) 1

Since the rank of the given matrix is 2, the value of 3 order determinant is zero.

Now