Which condition ensures a matrix is non-singular?

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Boost your skills in A Level Further Mathematics Core Pure. Study with flashcards and multiple choice questions, each question is followed by hints and explanations. Get prepared for your exam with confidence!

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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