For the matrix M = \begin{pmatrix} 4 & 2 \ 6 & 3 \end{pmatrix}, the determinant equals zero. What does this indicate about matrix M?

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Question

For the matrix M = \begin{pmatrix} 4 & 2 \ 6 & 3 \end{pmatrix}, the determinant equals zero. What does this indicate about matrix M?

Accepted Answer

M is a singular matrix — Award 1 mark for identifying that a matrix with determinant zero is singular and has no inverse. A is incorrect — the identity matrix has determinant 1. B is incorrect — a matrix with determinant zero does NOT have an inverse. D is incorrect — a diagonal matrix has non-zero elements only on the main diagonal.

Answer

M is a diagonal matrix

Answer

M has an inverse

Answer

M is a singular matrix

Answer

M is an identity matrix

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