Which condition ensures a matrix is non-singular?

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Prepare for the A Level Further Mathematics Core Pure Exam. Practice with flashcards and multiple-choice questions, each accompanied by hints and explanations. Ace your exam!

Multiple Choice

Which condition ensures a matrix is non-singular?

Explanation:
A matrix is non-singular exactly when its determinant is not zero. When det(M) ≠ 0, the matrix has full rank, its columns are linearly independent, and an inverse exists, so the transformation is invertible and does not collapse space. If det(M) = 0, the transformation collapses a dimension, there is a nontrivial solution to Mx = 0, and no inverse exists, so the matrix is singular. Symmetry can occur for singular cases, and being the identity is just a specific invertible example; the universal condition for non-singularity is det M ≠ 0.

A matrix is non-singular exactly when its determinant is not zero. When det(M) ≠ 0, the matrix has full rank, its columns are linearly independent, and an inverse exists, so the transformation is invertible and does not collapse space. If det(M) = 0, the transformation collapses a dimension, there is a nontrivial solution to Mx = 0, and no inverse exists, so the matrix is singular. Symmetry can occur for singular cases, and being the identity is just a specific invertible example; the universal condition for non-singularity is det M ≠ 0.

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