21.3.6. Properties

Try these first

1. 1.

   What is required for two matrices to be added together?

   Hint

   Consider how the structure of matrices is defined.

2. 2.

   What happens to each element of a matrix during scalar multiplication?

   Hint

   Think about the concept of scaling.

3. 3.

   What operation can only be performed on matrices of the same dimension?

   • A) Matrix multiplication
   • B) Matrix addition
   • C) Matrix inversion

   Hint

   Consider how matrices are structured.

4. 4.

   True or False: The determinant of a matrix can help determine if it's invertible.

   • True
   • False

   Hint

   Think about the relationship between determinant value and invertibility.

5. 5.

   If A is a 3x3 matrix with det(A) = 6, and B is a 3x3 matrix with det(B) = 2, calculate the determinant of AB and check if it is singular.

   Hint

   Use the property of determinants for the product of matrices.

6. 6.

   Consider matrix C = [[2, -1], [4, 3]]. Determine whether it's singular or non-singular and explain why.

   Hint

   Recall how to calculate the determinant for a 2x2 matrix.