Question

Let \(A\) be a \(3\times3\) matrix. If \[ A \begin{bmatrix} 001 \end{bmatrix} = \begin{bmatrix} 123 \end{bmatrix}, \quad A \begin{bmatrix} 101 \end{bmatrix} = \begin{bmatrix} 10-1 \end{bmatrix}, \quad A \begin{bmatrix} 110 \end{bmatrix} = \begin{bmatrix} 110 \end{bmatrix}, \] then the rank of \((A-I)\) is

• A. \(3\)
• B. \(2\)
• C. \(1\)
• D. \(0\)

Hint:

Whenever images of vectors under a matrix are given, first determine the columns of the matrix and then evaluate the required rank or determinant.

Answer 1

The Correct Option is B