Exercise

Here are two benefits of exercise:

1. Improved Mood:

   Exercise can stimulate the release of endorphins, which are chemicals in the brain that act as natural painkillers and mood elevators. Regular physical activity can help reduce stress, anxiety, and symptoms of depression.

   • Source: Mayo Clinic - Exercise and depression
2. Weight Management:

   Exercise helps burn calories, which is crucial for maintaining or losing weight. It also increases muscle mass, which boosts metabolism and helps the body burn more calories even when at rest. Consistent physical activity, combined with a balanced diet, can lead to effective weight management.

   • Source: CDC - Benefits of Physical Activity

No, a square matrix A is not invertible if its determinant |A| is equal to 0. A matrix is invertible (also known as non-singular or non-degenerate) if and only if its determinant is non-zero. If the determinant is zero, the matrix is singular and does not have an inverse.

Invertibility requires that the matrix represents a transformation that can be "undone." When the determinant is zero, it means the matrix collapses space (or at least reduces its dimension), making it impossible to reverse the transformation uniquely.

You can explore more about invertible matrices and their properties on websites such as:

• MathWorld: Invertible Matrix
• Wikipedia: Invertible Matrix