25.12.1. Singular Matrix

Try these first

1. 1.

   What defines a singular matrix?

   Hint

   Think about the matrix not having an inverse.

2. 2.

   Is the determinant of a non-singular matrix ever zero?

   Hint

   Consider what a non-singular matrix allows.

3. 3.

   What does a singular matrix indicate?

   • It has a non-zero determinant
   • It has infinitely many solutions
   • It cannot be inverted

   Hint

   Remember the consequences of zero determinants.

4. 4.

   True or False: A singular matrix can have a unique solution.

   • True
   • False

   Hint

   Consider what singular means.

5. 5.

   Given the system of equations: 2x + 3y = 5 and 4x + 6y = 10, determine if the matrix is singular or not. Explain the reasoning.

   Hint

   Use matrix determinants to analyze the coefficients.

6. 6.

   Suppose you needed to analyze a structural system in civil engineering. The stiffness matrix resulted in a singular configuration. What steps could you take to address this issue?

   Hint

   Think about what structural integrity demands.